Faithfulness and learning hypergraphs from discrete distributions
Klimova A, Uhler C, Rudas T. 2015. Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. 87(7), 57–72.
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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.
Publishing Year
Date Published
2015-07-01
Journal Title
Computational Statistics & Data Analysis
Publisher
Elsevier
Volume
87
Issue
7
Page
57 - 72
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Klimova A, Uhler C, Rudas T. Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. 2015;87(7):57-72. doi:10.1016/j.csda.2015.01.017
Klimova, A., Uhler, C., & Rudas, T. (2015). Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. Elsevier. https://doi.org/10.1016/j.csda.2015.01.017
Klimova, Anna, Caroline Uhler, and Tamás Rudas. “Faithfulness and Learning Hypergraphs from Discrete Distributions.” Computational Statistics & Data Analysis. Elsevier, 2015. https://doi.org/10.1016/j.csda.2015.01.017.
A. Klimova, C. Uhler, and T. Rudas, “Faithfulness and learning hypergraphs from discrete distributions,” Computational Statistics & Data Analysis, vol. 87, no. 7. Elsevier, pp. 57–72, 2015.
Klimova A, Uhler C, Rudas T. 2015. Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis. 87(7), 57–72.
Klimova, Anna, et al. “Faithfulness and Learning Hypergraphs from Discrete Distributions.” Computational Statistics & Data Analysis, vol. 87, no. 7, Elsevier, 2015, pp. 57–72, doi:10.1016/j.csda.2015.01.017.
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