Tractable structure search in the presence of latent variables

The problem of learning the structure of a DAG model in the presence of latent variables presents many formidable challenges. In particular there are an innnite number of latent variable models to consider, and these models possess features which make them hard to work with. We describe a class of graphical models which can represent the conditional independence structure induced by a latent variable model over the observed margin. We give a parametrization of the set of Gaussian distributions with conditional independence structure given by a MAG model. The models are illustrated via a simple example. Different estimation techniques are discussed in the context of Zellner's Seemingly Unrelated Regression (SUR) models.