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arXiv · 1404.6617

Faithfulness and learning hypergraphs from discrete distributions

Anna Klimova·Caroline Uhler·Tamas Rudas
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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.

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Anna Klimova, Caroline Uhler, Tamas Rudas. 2015-01-23. Faithfulness and learning hypergraphs from discrete distributions. https://arxiv.org/abs/1404.6617

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