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现实世界现象中，平衡状态通常用图模型中的循环来表示。一种具有表达力的图模型——关系因果模型，能够表示并推理包含此类循环或反馈环路的复杂动态系统。现有的基于观测数据学习因果模型的循环因果发现算法假设数据实例独立同分布，这使得它们不适用于关系因果模型。同时，面向关系因果模型的因果发现算法则假设无环性。本研究探讨了在何种必要且充分的条件下，基于约束的关系因果发现算法对于循环关系因果模型是正确且完备的。我们引入了关系去循环化——一种专为关系模型设计的操作，能够推理循环关系因果模型的可辨识性。我们证明，在关系去循环化和σ-忠实性假设下，关系因果发现算法RCD（Maier等人，2013年）对于循环模型是正确且完备的。我们通过实验结果支持这一论断。