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- W2259391444 abstract "Information-related measures are important tools of multi-variable data analysis, as measures of dependence among variables and the description of order in biological and physical systems. Informtion-related measures, like marginal entropies, mutual / interaction / multi-information, are also relevant to the theory of complexity of systems and biological data analysis. The mathematical properties and relationships among these measures are therefore of significant interest. A number of interesting relations between common information measures include the duality relations based on Mobius inversion on lattices, which are the direct consequence of the symmetries of the lattices (subsets ordered by inclusion) of the sets of variables. In this paper we define operators on functions on these lattices that map the functions into one another, called Mobius operators. We show that these operators define a simple group isomorphic to the symmetric group S3. Relations among the set of functions on the lattice are transparently expressed in terms of this operator algebra, and when applied to the information measures, can be used to describe relationships among measures useful in data analysis, including conditional probabilities. We describe a direct relation between sums of conditional log-likelihoods and previously defined dependency/complexity measures. The algebra can be generalized by defining operators for all possible lattice reference elements (subsets), which yields a general set of relationships more extensive and inclusive than the usual Mobius inversion relations. This formalism provides a fundamental unification of information-related measures. Isomorphism of all distributive lattices with the subset lattice implies broad potential application of these results." @default.
- W2259391444 created "2016-06-24" @default.
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- W2259391444 date "2016-01-25" @default.
- W2259391444 modified "2023-09-27" @default.
- W2259391444 title "Unifying formalism for multivariate information-related measures: Möbius operators on subset lattices." @default.
- W2259391444 hasPublicationYear "2016" @default.
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