Graphs for Margins of Bayesian Networks

Abstract

Directed acyclic graph (DAG) models—also called Bayesian networks—are widely used in probabilistic reasoning, machine learning and causal inference. If latent variables are present, then the set of possible marginal distributions over the remaining (observed) variables is generally not represented by any DAG. Larger classes of mixed graphical models have been introduced to overcome this; however, as we show, these classes are not sufficiently rich to capture all the marginal models that can arise. We introduce a new class of hyper-graphs, called mDAGs, and a latent projection operation to obtain an mDAG from the margin of a DAG. We show that each distinct marginal of a DAG model is represent..