When some variables in a directed acyclic graph (DAG) are hidden, a notoriously complicated set of constraints on the distribution of observed variables is implied. In this talk, we present inequality constraints implied by graphical criteria in hidden variable DAGs. For DAGs that exhibit e-separation relations, we present entropic inequality constraints and we show how they can be used to learn about the true causal model from an observed data distribution (arXiv:2107.07087). For DAGs that exhibit d-separation relations and with a promise that unobserved variables have known cardinalities, we present inequality constraints that resemble constraints present in models that involve quantum systems (arXiv:2109.05656).

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