Latent-free equivalent mDAGs

TL;DR

This paper demonstrates that for discrete DAGs with hidden variables, the marginal model is equivalent to a fully observable DAG model precisely when no non-trivial inequality constraints are induced.

Contribution

It provides a characterization of when hidden variables in discrete DAGs do not impose additional inequality constraints, linking marginal models to fully observable DAGs.

Findings

Marginal models are equivalent to fully observable DAGs without inequality constraints.

Distributional equivalence depends on the absence of non-trivial inequalities.

Characterizes conditions for equivalence in discrete DAG models.

Abstract

We show that the marginal model for a discrete directed acyclic graph (DAG) with hidden variables is distributionally equivalent to another fully observable DAG model if and only if it does not induce any non-trivial inequality constraints.