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。

关系因果模型的提升表示：推理和结构学习的影响再探讨

Lifted Representation of Relational Causal Models Revisited:  Implications for Reasoning and Structure Learning

We extend the theory of d-separation to cases in which data instances are not
independent and identically distributed. We show that applying the rules of
d-separation directly to the structure of probabilistic models of relational
data inaccurately infers conditional independence. We introduce relational
d-separation, a theory for deriving conditional independence facts from
relational models. We provide a new representation, the abstract ground graph,
that enables a sound, complete, and computationally efficient method for
answering d-separation queries about relational models, and we present
empirical results that demonstrate effectiveness.

本文在不独立于同分布的数据实例上扩展了 d 分离理论，引入关系分离理论以从 relational models 推导条件独立性并提出了抽象的 ground graph 表达方式，从而实现了一种可靠、完整、高效的计算 d-separation 查询的方法。