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。

聚类 DAG 中的因果效应识别

Causal Effect Identification in Cluster DAGs

The term "interference" has been used to describe any setting in which one
subject's exposure may affect another subject's outcome. We use causal diagrams
to distinguish among three causal mechanisms that give rise to interference.
The first causal mechanism by which interference can operate is a direct causal
effect of one individual's treatment on another individual's outcome; we call
this direct interference. Interference by contagion is present when one
individual's outcome may affect the outcomes of other individuals with whom he
comes into contact. Then giving treatment to the first individual could have an
indirect effect on others through the treated individual's outcome. The third
pathway by which interference may operate is allocational interference.
Treatment in this case allocates individuals to groups; through interactions
within a group, individuals may affect one another's outcomes in any number of
ways. In many settings, more than one type of interference will be present
simultaneously. The causal effects of interest differ according to which types
of interference are present, as do the conditions under which causal effects
are identifiable. Using causal diagrams for interference, we describe these
differences, give criteria for the identification of important causal effects,
and discuss applications to infectious diseases.

本文使用因果图来区分三种引起干扰的因果机制：直接干扰、接触传染的干扰和分配干扰，说明了这些不同类型的干扰所涉及的因果效应以及识别它们的条件，并讨论了其在传染病方面的应用。