2014年7月
Duality of Maximum Entropy and Minimum Divergence
ENTROPY
- ,
- ,
- 巻
- 16
- 号
- 7
- 開始ページ
- 3552
- 終了ページ
- 3572
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.3390/e16073552
- 出版者・発行元
- MDPI AG
We discuss a special class of generalized divergence measures by the use of generator functions. Any divergence measure in the class is separated into the difference between cross and diagonal entropy. The diagonal entropy measure in the class associates with a model of maximum entropy distributions; the divergence measure leads to statistical estimation via minimization, for arbitrarily giving a statistical model. The dualistic relationship between the maximum entropy model and the minimum divergence estimation is explored in the framework of information geometry. The model of maximum entropy distributions is characterized to be totally geodesic with respect to the linear connection associated with the divergence. A natural extension for the classical theory for the maximum likelihood method under the maximum entropy model in terms of the Boltzmann-Gibbs-Shannon entropy is given. We discuss the duality in detail for Tsallis entropy as a typical example.
- リンク情報
- ID情報
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- DOI : 10.3390/e16073552
- ISSN : 1099-4300
- Web of Science ID : WOS:000339990800001