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Qualité d’un graphe implicatif : variance implicative

Abstract : A weighted Directed Acyclic Graph offers a useful representation for a set of implication rules which are extracted from dataset. In such a weighted DAG, vertices are the binary variables describing the data, arcs the rules, and arc values their intensities of implication. The relevance of the DAG for expert interpretations is a challenging issue, since the threshold for rule selection may vary and shall be set properly. Here we present the concept of implicative variance in order to assess the relevance of the DAG depending on the threshold value. It is based on a repulsive metaphor versus implicative mutual consistency between two binary variables, computed from their symmetric difference.
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Contributor : Jean-Claude Regnier <>
Submitted on : Tuesday, October 17, 2017 - 11:35:01 AM
Last modification on : Tuesday, January 5, 2021 - 4:26:09 PM


  • HAL Id : hal-01617928, version 1


Jean-Claude Regnier, Régis Gras. Qualité d’un graphe implicatif : variance implicative . Régis Gras, Jean-Claude Régnier, Dominique Lahanier-Reuter, Claudia Marinica, Fabrice Guillet. L'analyse statistique implicative. Des Sciences dures aux Sciences Humaines et Sociales, Cépaduès Editions, pp.253-264, 2017, 978.2.36493.577.8. ⟨hal-01617928⟩



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