Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the distribution of observed variables. In this work, we present entropic inequality constraints that are implied by $e$-separation relations in hidden variable DAGs with discrete observed variables. The constraints can intuitively be understood to follow from the fact that the capacity of variables along a causal pathway to convey information is restricted by their entropy; e.g. at the extreme case, a variable with entropy $0$ can convey no information. We show how these constraints can be used to learn about the true causal model from an observed data distribution. In addition, we propose a measure of causal influence called the minimal mediary entropy, and demonstrate that it can augment traditional measures such as the average causal effect.

翻译：含隐变量的有向无环图（DAGs）常用于刻画系统中变量间的因果关联。当某些变量不可观测时，DAG会蕴含一组关于观测变量分布的复杂约束条件。本研究提出由离散观测变量隐变量DAG中$e$-分离关系所蕴含的熵不等式约束。这些约束可直观理解为：因果路径上的变量传递信息的能力受限于其熵值——例如在极端情况下，熵值为$0$的变量无法传递任何信息。我们论证了如何利用这些约束从观测数据分布中推断真实因果模型。此外，提出一种名为最小中介熵的因果效应度量，并证明其能增强平均因果效应等传统度量方法的分析能力。