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Directed acyclic graphs (DAGs) with hidden variables are often used tocharacterize causal relations between variables in a system. When somevariables are unobserved, DAGs imply a notoriously complicated set ofconstraints on the distribution of observed variables. In this work, we presententropic inequality constraints that are implied by $e$-separation relations inhidden variable DAGs with discrete observed variables. The constraints canintuitively be understood to follow from the fact that the capacity ofvariables along a causal pathway to convey information is restricted by theirentropy; e.g. at the extreme case, a variable with entropy $0$ can convey noinformation. We show how these constraints can be used to learn about the truecausal model from an observed data distribution. In addition, we propose ameasure of causal influence called the minimal mediary entropy, and demonstratethat it can augment traditional measures such as the average causal effect.

Entropic Inequality Constraints from $e$-separation Relations in Directed Acyclic Graphs with Hidden Variables