Testing Unfaithful Gaussian Graphical Models

Part of Advances in Neural Information Processing Systems 27 (NIPS 2014)

Authors

De Wen Soh, Sekhar Tatikonda

Abstract

The global Markov property for Gaussian graphical models ensures graph separation implies conditional independence. Specifically if a node set $S$ graph separates nodes $u$ and $v$ then $X_u$ is conditionally independent of $X_v$ given $X_S$. The opposite direction need not be true, that is, $X_u \perp X_v \mid X_S$ need not imply $S$ is a node separator of $u$ and $v$. When it does, the relation $X_u \perp X_v \mid X_S$ is called faithful. In this paper we provide a characterization of faithful relations and then provide an algorithm to test faithfulness based only on knowledge of other conditional relations of the form $X_i \perp X_j \mid X_S$.