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：在涉及相互关联单位之间相互影响或因果效应的现实世界现象中,均衡状态通常在图形模型中以循环方式呈现。一个显示式的图形模型类别、关系因果模型,可以代表展示这种循环或反馈环状的复杂动态系统并解释其原因。从观察数据中学习因果模型的现有循环因果发现算法假定数据实例是独立的,分布相同,因此不适合关联因果模型。同时,关系因果模型的因果发现算法假定周期性。在这项工作中,我们研究了基于约束性因果发现算法对于循环因果模型来说是合理和完整的必要和充分条件。我们引入了关系循环循环因果计算法,这是专门为关系模型设计的一种关联性计算方法,有助于推理循环因果模型的可识别性。我们证明,根据关系循环周期化假设和美美利美的假设,关系因果解算法(Maier等人,2013年)对于循环模型来说是合理和完整的。我们提出了支持我们主张的实验结果。