Reasoning about the effect of interventions and counterfactuals is a
fundamental task found throughout the data sciences. A collection of
principles, algorithms, and tools has been developed for performing such tasks
in the last decades (Pearl, 2000). One of the pervasive requirements found
throughout this literature is the articulation of assumptions, which commonly
appear in the form of causal diagrams. Despite the power of this approach,
there are significant settings where the knowledge necessary to specify a
causal diagram over all variables is not available, particularly in complex,
high-dimensional domains. In this paper, we introduce a new graphical modeling
tool called cluster DAGs (for short, C-DAGs) that allows for the partial
specification of relationships among variables based on limited prior
knowledge, alleviating the stringent requirement of specifying a full causal
diagram. A C-DAG specifies relationships between clusters of variables, while
the relationships between the variables within a cluster are left unspecified,
and can be seen as a graphical representation of an equivalence class of causal
diagrams that share the relationships among the clusters. We develop the
foundations and machinery for valid inferences over C-DAGs about the clusters
of variables at each layer of Pearl's Causal Hierarchy (Pearl and Mackenzie
2018; Bareinboim et al. 2020) - L1 (probabilistic), L2 (interventional), and L3
(counterfactual). In particular, we prove the soundness and completeness of
d-separation for probabilistic inference in C-DAGs. Further, we demonstrate the
validity of Pearl's do-calculus rules over C-DAGs and show that the standard ID
identification algorithm is sound and complete to systematically compute causal
effects from observational data given a C-DAG. Finally, we show that C-DAGs are
valid for performing counterfactual inferences about clusters of variables.

该研究介绍了一种叫做 “集群有向无环图（Cluster DAGs）” 的新型图形建模工具，其可以基于有限的先验知识提供变量之间关系的部分规范，从而缓解了在复杂、高维度领域中指定完全因果图的严格要求。在该图形模型下，本研究还开发了基于 “Pearl's Causal Hierarchy” 的各层级的变量集聚进行推理的方法，并验证了 C-DAGs 的有效性。