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