Information Geometric Duality of ϕ-Deformed Exponential Families

15780 8 86790 2 246553 document 86790 entropy-21-00112.pdf application/pdf 067ecb6f9c20d8ba9b75f05a353230b6 MD5 1630673 2019-03-04 14:28:45 https://pure.iiasa.ac.at/id/eprint/15780/1/entropy-21-00112.pdf 15780 1 1 application/pdf text en public cc_by_4

entropy-21-00112.pdf

published 86796 1 246565 document 86796 indexcodes.txt text/x-c++ 2ebe4149b50c33b538bf208abe9f7c7d MD5 6658 2019-03-04 14:38:27 https://pure.iiasa.ac.at/id/eprint/15780/2/indexcodes.txt 15780 2 2 text/x-c++ other Generate index codes conversion from text to indexcodes en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/86790 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/86790 http://eprints.org/relation/issmallThumbnailVersionOf https://pure.iiasa.ac.at/id/document/86790 archive 353 disk0/00/01/57/80 2019-03-04 14:30:16 2021-08-27 17:31:29 2019-03-04 14:30:16 article show Korbel J. Hanel R. Thurner S. 1918 Information Geometric Duality of ϕ-Deformed Exponential Families pub prog_asa generalized entropy; ϕ-deformed family; Fisher information; information geometry; Cramér–Rao bound; (c,d)-entropy In the world of generalized entropies—which, for example, play a role in physical systems with sub- and super-exponential phase space growth per degree of freedom—there are two ways for implementing constraints in the maximum entropy principle: linear and escort constraints. Both appear naturally in different contexts. Linear constraints appear, e.g., in physical systems, when additional information about the system is available through higher moments. Escort distributions appear naturally in the context of multifractals and information geometry. It was shown recently that there exists a fundamental duality that relates both approaches on the basis of the corresponding deformed logarithms (deformed-log duality). Here, we show that there exists another duality that arises in the context of information geometry, relating the Fisher information of ϕ -deformed exponential families that correspond to linear constraints (as studied by J.Naudts) to those that are based on escort constraints (as studied by S.-I. Amari). We explicitly demonstrate this information geometric duality for the case of (c,d) -entropy, which covers all situations that are compatible with the first three Shannon–Khinchin axioms and that include Shannon, Tsallis, Anteneodo–Plastino entropy, and many more as special cases. Finally, we discuss the relation between the deformed-log duality and the information geometric duality and mention that the escort distributions arising in these two dualities are generally different and only coincide for the case of the Tsallis deformation. 2019-02-01 published Molecular Diversity Preservation International (MDPI) 10.3390/e21020112 307 public Entropy 21 2 112 TRUE 1099-4300 FALSE no info:eu-repo/semantics/article