Matches in SemOpenAlex for { <https://semopenalex.org/work/W4287068287> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W4287068287 abstract "Tsallis and R'{e}nyi entropies, which are monotone transformations of each other, are deformations of the celebrated Shannon entropy. Maximization of these deformed entropies, under suitable constraints, leads to the $q$-exponential family which has applications in non-extensive statistical physics, information theory and statistics. In previous information-geometric studies, the $q$-exponential family was analyzed using classical convex duality and Bregman divergence. In this paper, we show that a generalized $lambda$-duality, where $lambda = 1 - q$ is the constant information-geometric curvature, leads to a generalized exponential family which is essentially equivalent to the $q$-exponential family and has deep connections with R'{e}nyi entropy and optimal transport. Using this generalized convex duality and its associated logarithmic divergence, we show that our $lambda$-exponential family satisfies properties that parallel and generalize those of the exponential family. Under our framework, the R'{e}nyi entropy and divergence arise naturally, and we give a new proof of the Tsallis/R'{e}nyi entropy maximizing property of the $q$-exponential family. We also introduce a $lambda$-mixture family which may be regarded as the dual of the $lambda$-exponential family, and connect it with other mixture-type families. Finally, we discuss a duality between the $lambda$-exponential family and the $lambda$-logarithmic divergence, and study its statistical consequences." @default.
- W4287068287 created "2022-07-25" @default.
- W4287068287 creator A5053260623 @default.
- W4287068287 creator A5071672663 @default.
- W4287068287 date "2021-07-25" @default.
- W4287068287 modified "2023-10-17" @default.
- W4287068287 title "Tsallis and R'{e}nyi deformations linked via a new $lambda$-duality" @default.
- W4287068287 doi "https://doi.org/10.48550/arxiv.2107.11925" @default.
- W4287068287 hasPublicationYear "2021" @default.
- W4287068287 type Work @default.
- W4287068287 citedByCount "0" @default.
- W4287068287 crossrefType "posted-content" @default.
- W4287068287 hasAuthorship W4287068287A5053260623 @default.
- W4287068287 hasAuthorship W4287068287A5071672663 @default.
- W4287068287 hasBestOaLocation W42870682871 @default.
- W4287068287 hasConcept C106301342 @default.
- W4287068287 hasConcept C112680207 @default.
- W4287068287 hasConcept C114614502 @default.
- W4287068287 hasConcept C117521176 @default.
- W4287068287 hasConcept C121332964 @default.
- W4287068287 hasConcept C134306372 @default.
- W4287068287 hasConcept C149073432 @default.
- W4287068287 hasConcept C151376022 @default.
- W4287068287 hasConcept C202444582 @default.
- W4287068287 hasConcept C2524010 @default.
- W4287068287 hasConcept C2778023678 @default.
- W4287068287 hasConcept C2778113609 @default.
- W4287068287 hasConcept C2780056601 @default.
- W4287068287 hasConcept C28826006 @default.
- W4287068287 hasConcept C33923547 @default.
- W4287068287 hasConcept C39927690 @default.
- W4287068287 hasConcept C55974624 @default.
- W4287068287 hasConcept C62520636 @default.
- W4287068287 hasConceptScore W4287068287C106301342 @default.
- W4287068287 hasConceptScore W4287068287C112680207 @default.
- W4287068287 hasConceptScore W4287068287C114614502 @default.
- W4287068287 hasConceptScore W4287068287C117521176 @default.
- W4287068287 hasConceptScore W4287068287C121332964 @default.
- W4287068287 hasConceptScore W4287068287C134306372 @default.
- W4287068287 hasConceptScore W4287068287C149073432 @default.
- W4287068287 hasConceptScore W4287068287C151376022 @default.
- W4287068287 hasConceptScore W4287068287C202444582 @default.
- W4287068287 hasConceptScore W4287068287C2524010 @default.
- W4287068287 hasConceptScore W4287068287C2778023678 @default.
- W4287068287 hasConceptScore W4287068287C2778113609 @default.
- W4287068287 hasConceptScore W4287068287C2780056601 @default.
- W4287068287 hasConceptScore W4287068287C28826006 @default.
- W4287068287 hasConceptScore W4287068287C33923547 @default.
- W4287068287 hasConceptScore W4287068287C39927690 @default.
- W4287068287 hasConceptScore W4287068287C55974624 @default.
- W4287068287 hasConceptScore W4287068287C62520636 @default.
- W4287068287 hasLocation W42870682871 @default.
- W4287068287 hasOpenAccess W4287068287 @default.
- W4287068287 hasPrimaryLocation W42870682871 @default.
- W4287068287 hasRelatedWork W2260035625 @default.
- W4287068287 hasRelatedWork W2330900335 @default.
- W4287068287 hasRelatedWork W2386628002 @default.
- W4287068287 hasRelatedWork W2602807540 @default.
- W4287068287 hasRelatedWork W2969036527 @default.
- W4287068287 hasRelatedWork W3097388336 @default.
- W4287068287 hasRelatedWork W4287068287 @default.
- W4287068287 hasRelatedWork W4290720396 @default.
- W4287068287 hasRelatedWork W4297404811 @default.
- W4287068287 hasRelatedWork W4287610888 @default.
- W4287068287 isParatext "false" @default.
- W4287068287 isRetracted "false" @default.
- W4287068287 workType "article" @default.