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.

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

Learning Relational Causal Models with Cycles through Relational Acyclification

We show how, and under which conditions, the equilibrium states of a
first-order Ordinary Differential Equation (ODE) system can be described with a
deterministic Structural Causal Model (SCM). Our exposition sheds more light on
the concept of causality as expressed within the framework of Structural Causal
Models, especially for cyclic models.

本研究通过确定性结构因果模型描述一阶常微分方程系统的平衡状态并阐明了其因果关系概念，尤其适用于循环模型。