In real-world phenomena which involve mutual influence or causal effects between interconnected units, equilibrium states are typically represented with cycles in graphical models. An expressive class of graphical models, relational causal models, can represent and reason about complex dynamic systems exhibiting such cycles or feedback loops. Existing cyclic causal discovery algorithms for learning causal models from observational data assume that the data instances are independent and identically distributed which makes them unsuitable for relational causal models. At the same time, causal discovery algorithms for relational causal models assume acyclicity. In this work, we examine the necessary and sufficient conditions under which a constraint-based relational causal discovery algorithm is sound and complete for cyclic relational causal models. We introduce relational acyclification, an operation specifically designed for relational models that enables reasoning about the identifiability of cyclic relational causal models. We show that under the assumptions of relational acyclification and $\sigma$-faithfulness, the relational causal discovery algorithm RCD (Maier et al. 2013) is sound and complete for cyclic models. We present experimental results to support our claim.

翻译：在涉及相互影响或因果效应的真实世界现象中，互连单元间的平衡状态通常用图模型中的环来表示。关系因果模型作为一种表达能力强的图模型，能够表示和推理存在此类环或反馈环路的复杂动态系统。现有基于观测数据学习因果模型的环发现算法假设数据实例独立同分布，这使其不适用于关系因果模型。同时，关系因果模型的因果发现算法又假设无环性。在本研究中，我们检验了基于约束的关系因果发现算法在带环关系因果模型下成立且完备的充分必要条件。我们提出了关系去环化操作，该操作专为关系模型设计，能够推理带环关系因果模型的可识别性。我们证明，在关系去环化与$\sigma$-忠实性假设下，关系因果发现算法RCD（Maier等，2013）对带环模型成立且完备。我们通过实验验证了这一结论。