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Faithfulness and learning hypergraphs from discrete distributions

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  • Klimova, Anna
  • Uhler, Caroline
  • Rudas, Tamás

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.

Suggested Citation

  • Klimova, Anna & Uhler, Caroline & Rudas, Tamás, 2015. "Faithfulness and learning hypergraphs from discrete distributions," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 57-72.
    • Handle: RePEc:eee:csdana:v:87:y:2015:i:c:p:57-72
    DOI: 10.1016/j.csda.2015.01.017
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    References listed on IDEAS

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    1. David Edwards, 2012. "A note on adding and deleting edges in hierarchical log-linear models," Computational Statistics, Springer, vol. 27(4), pages 799-803, December.
    2. James M. Robins, 2003. "Uniform consistency in causal inference," Biometrika, Biometrika Trust, vol. 90(3), pages 491-515, September.
    3. Peter Spirtes & Clark Glymour & Richard Scheines, 2001. "Causation, Prediction, and Search, 2nd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262194406, April.
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