While feedback loops are known to play important roles in many complex systems, their existence is ignored in a large part of the causal discovery literature, as systems are typically assumed to be acyclic from the outset. When applying causal discovery algorithms designed for the acyclic setting on data generated by a system that involves feedback, one would not expect to obtain correct results. In this work, we show that -- surprisingly -- the output of the Fast Causal Inference (FCI) algorithm is correct if it is applied to observational data generated by a system that involves feedback. More specifically, we prove that for observational data generated by a simple and $\sigma$-faithful Structural Causal Model (SCM), FCI is sound and complete, and can be used to consistently estimate (i) the presence and absence of causal relations, (ii) the presence and absence of direct causal relations, (iii) the absence of confounders, and (iv) the absence of specific cycles in the causal graph of the SCM. We extend these results to constraint-based causal discovery algorithms that exploit certain forms of background knowledge, including the causally sufficient setting (e.g., the PC algorithm) and the Joint Causal Inference setting (e.g., the FCI-JCI algorithm).

翻译：尽管反馈回路在许多复杂系统中扮演重要角色，但大部分因果发现文献都忽略了它们的存在，因为通常从一开始就假定系统是无环的。当将针对无环场景设计的因果发现算法应用于涉及反馈系统生成的数据时，我们无法期望得到正确结果。在本工作中，我们表明——令人惊讶的是——当将快速因果推断（FCI）算法应用于涉及反馈系统生成的观测数据时，其输出是正确的。具体而言，我们证明：对于由简单且σ-忠实结构因果模型（SCM）生成的观测数据，FCI是可靠且完备的，可用于一致地估计（i）因果关系的有无、（ii）直接因果关系的有无、（iii）混杂因素的不存在性，以及（iv）SCM因果图中特定环的不存在性。我们将这些结果扩展至利用特定形式背景知识的基于约束的因果发现算法，包括因果充分场景（如PC算法）和联合因果推断场景（如FCI-JCI算法）。