Faithfulness and learning hypergraphs from discrete distributions
Abstract
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-linear models are considered instead, and the concept of parametric (strong-) faithfulness with respect to a hypergraph is introduced. Strong-faithfulness ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association.
Keywords
Cite
@article{arxiv.1404.6617,
title = {Faithfulness and learning hypergraphs from discrete distributions},
author = {Anna Klimova and Caroline Uhler and Tamas Rudas},
journal= {arXiv preprint arXiv:1404.6617},
year = {2015}
}
Comments
23 pages, 6 figures