| 来源类型 | Article |
| 规范类型 | 其他 |
| DOI | 10.3390/e21020112 |
| Information Geometric Duality of ϕ-Deformed Exponential Families. | |
| Korbel J; Hanel R; Thurner S | |
| 发表日期 | 2019 |
| 出处 | Entropy 21 (2): p. 112 |
| 出版年 | 2019 |
| 语种 | 英语 |
| 摘要 | 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. |
| 主题 | Advanced Systems Analysis (ASA) |
| 关键词 | generalized entropy ϕ-deformed family Fisher information information geometry Cramér–Rao bound (c,d)-entropy |
| URL | http://pure.iiasa.ac.at/id/eprint/15780/ |
| 来源智库 | International Institute for Applied Systems Analysis (Austria) |
| 引用统计 | |
| 资源类型 | 智库出版物 |
| 条目标识符 | http://119.78.100.153/handle/2XGU8XDN/131595 |
| 推荐引用方式 GB/T 7714 | Korbel J,Hanel R,Thurner S. Information Geometric Duality of ϕ-Deformed Exponential Families.. 2019. |
| 条目包含的文件 | ||||||
| 文件名称/大小 | 资源类型 | 版本类型 | 开放类型 | 使用许可 | ||
| entropy-21-00112.pdf（1592KB） | 智库出版物 | 限制开放 | CC BY-NC-SA | 浏览 | ||
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