Causal reasoning in relational domains is fundamental to studying real-world
social phenomena in which individual units can influence each other's traits
and behavior. Dynamics between interconnected units can be represented as an
instantiation of a relational causal model; however, causal reasoning over such
instantiation requires additional templating assumptions that capture feedback
loops of influence. Previous research has developed lifted representations to
address the relational nature of such dynamics but has strictly required that
the representation has no cycles. To facilitate cycles in relational
representation and learning, we introduce relational $\sigma$-separation, a new
criterion for understanding relational systems with feedback loops. We also
introduce a new lifted representation, $\sigma$-abstract ground graph which
helps with abstracting statistical independence relations in all possible
instantiations of the cyclic relational model. We show the necessary and
sufficient conditions for the completeness of $\sigma$-AGG and that relational
$\sigma$-separation is sound and complete in the presence of one or more cycles
with arbitrary length. To the best of our knowledge, this is the first work on
representation of and reasoning with cyclic relational causal models.

本文介绍了一种新的关于环形关系因果模型的表示方法和推理方法。通过引入关系 σ 分离的新标准，以及一种新的提升表示，σ- 抽象地面图，帮助在所有可能的实例化中抽象统计独立关系。我们还表明，基于 σ-AGG，关系 σ 分离对于任意长度的一个或多个循环的存在是完整的和有必要的。本文是有关现有研究所建立的第一个运行时表示和推理循环关系因果模型。

具有循环的关系因果模型：表示和推理

Relational Causal Models with Cycles:Representation and Reasoning

Maier et al. (2010) introduced the relational causal model (RCM) for
representing and inferring causal relationships in relational data. A lifted
representation, called abstract ground graph (AGG), plays a central role in
reasoning with and learning of RCM. The correctness of the algorithm proposed
by Maier et al. (2013a) for learning RCM from data relies on the soundness and
completeness of AGG for relational d-separation to reduce the learning of an
RCM to learning of an AGG. We revisit the definition of AGG and show that AGG,
as defined in Maier et al. (2013b), does not correctly abstract all ground
graphs. We revise the definition of AGG to ensure that it correctly abstracts
all ground graphs. We further show that AGG representation is not complete for
relational d-separation, that is, there can exist conditional independence
relations in an RCM that are not entailed by AGG. A careful examination of the
relationship between the lack of completeness of AGG for relational
d-separation and faithfulness conditions suggests that weaker notions of
completeness, namely adjacency faithfulness and orientation faithfulness
between an RCM and its AGG, can be used to learn an RCM from data.

本研究重新审视了抽象地面图的定义，确保其能正确地抽象所有地面图并表明其嵌套不完整，从而提出了更弱的完备性概念，即 RC 模型和其 AGG 之间的邻接完备性和方向完备性，以更好地从数据中学习 RC 模型。