ArticleEntropy (Basel, Switzerland)2019
Symmetries among Multivariate Information Measures Explored Using Möbius Operators.
Article in Entropy (Basel, Switzerland), 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information.Entropy (Basel, Switzerland) · 2023Article
- Toward an Information Theory of Quantitative Genetics.Journal of computational biology : a journal of computational molecular cell biology · 2021Article
- Computational Inference Software for Tetrad Assembly from Randomly Arrayed Yeast Colonies.G3 (Bethesda, Md.) · 2019Article
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2 authors.
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Abstract
Relations between common information measures include the duality relations based on Möbius inversion on lattices, which are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). In this paper we use the lattice and functional symmetries to provide a unifying formalism that reveals some new relations and systematizes the symmetries of the information functions. To our knowledge, this is the first systematic examination of the full range of relationships of this class of functions. We define operators on functions on these lattices based on the Möbius inversions that map functions into one another, which we call Möbius operators, and show that they form a simple group isomorphic to the symmetric group S
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