Faithfulness and learning hypergraphs from discrete distributions

The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linearmodels are considered instead, and the concept of parametric (strong-)faithfulnesswith respect to a hypergraph is introduced. The strength of association in a discrete distribution can be quantifiedwith variousmeasures, leading to different concepts of strong-faithfulness. It is proven that strongfaithfulness defined in terms of interaction parameters ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations andmeasures of association. © 2015 Elsevier B.V. All rights reserved.