2014/04/26 by Anna Klimova, Anna Klimová, Caroline Uhler +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Bioinformatics and Genomic Networks #Data Mining Algorithms and Applications #FOS: Computer and information sciences #Methodology (stat.ME) #stat.ME
paper · pdf · doi:10.48550/arxiv.1404.6617
23 pages, 6 figures
openalex publication_date 2014/04/26 · arxiv created 2015/01/23 · arxiv updated 2015/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.