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, \textit{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 \textit{cyclic relational causal models}. We introduce \textit{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.

在关系因果模型中，通过关系回路对复杂的动态系统进行建模和推理，本文引入了一种关系去环操作，探讨了用于循环关系因果模型的约束关系因果发现算法的充分必要条件。

通过关系消环来学习具有环的关系因果模型