One pervasive task found throughout the empirical sciences is to determine the effect of interventions from non-experimental data. It is well-understood that assumptions are necessary to perform causal inferences, which are commonly articulated through causal diagrams (Pearl, 2000). Despite the power of this approach, there are settings where the knowledge necessary to specify a causal diagram over all observed variables may not be available, particularly in complex, high-dimensional domains. In this paper, we introduce a new type of graphical model called cluster causal diagrams (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. We develop the foundations and machinery for valid causal inferences over C-DAGs. In particular, we first define a new version of the d-separation criterion and prove its soundness and completeness. Secondly, we extend these new separation rules and prove the validity of the corresponding do-calculus. Lastly, we show that a standard identification algorithm is sound and complete to systematically compute causal effects from observational data given a C-DAG.
翻译:在整个实验科学中发现的一项普遍任务是确定非实验性数据干预的效果。人们清楚地知道,为了进行因果推断,必须假设,而因果推断通常是通过因果图表表达的(Pearl,2000年)。尽管这种方法具有力量,但有些环境可能不具备为所有观察到的变数确定因果图表所需的知识,特别是在复杂、高维领域。在本文件中,我们引入了一种新的图形模型,称为群集因果图(短期的C-DAGs),允许根据有限的先前知识对变量之间的关系进行部分说明,减轻规定全面因果图表的严格要求。C-DAG规定了变量组之间的关系,而一个组内的变量之间的关系则没有说明。我们为C-DAGs的有效因果推断开发了基础和机制。特别是,我们首先定义了 d-分离标准标准因果图表的新版本,并证明了其准确性和完整性。第二,我们扩展了这些新的分离规则,并证明从给定的因果分析效果中完成对应的量化效果。C-D.AG.A.A.我们系统地展示了标准的因果分析结果。