 Faithfulness and learning hypergraphs from discrete distributionsAnna Klimova, Caroline Uhler and Tamás Rudas Computational Statistics & Data Analysis, 2015, vol. 87, issue C, 57-72 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. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. It is proven that strong-faithfulness 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 and measures of association. Keywords: Contingency tables; Directed acyclic graphs; Hierarchical log-linear models; Hypergraphs; (Strong-)faithfulness (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:87:y:2015:i:c:p:57-72 DOI: 10.1016/j.csda.2015.01.017 Access Statistics for this article Computational Statistics & Data Analysis is currently edited by S.P. Azen More articles in Computational Statistics & Data Analysis from Elsevier |
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