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- 甘利 俊一
- 東京大学工学部計数工学科
書誌事項
- タイトル別名
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- Information Geometry
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説明
Information geometry is a new theoretical method to elucidate intrinsic geometrical structures underlying information systems. It is applicable to wide areas of information sciences including statistics, information theory, systems theory, etc. More concretely, information geometry studies the intrinsic geometrical structure of the manifold of probability distributions. It is found that the manifold of probability distributions leads us to a new and rich differential geometrical theory. Since most of information sciences are closely related to probability distributions, it gives a powerful method to study their intrinsic structures. A manifold consisting of a smooth family of probability distributions has a unique invariant Riemannian metric given by the Fisher information. It admits a one-parameter family of invariant affine connections, called the α-connection, where α and-α-connections are dually coupled with the Riemannian metric. The duality in affine connections is a new concept in differential geometry. When a manifold is dually flat, it admits an invariant divergence measure for which a generalized Pythagorian theorem and a projection theorem hold. The dual structure of such manifolds can be applied to statistical inference, multiterminal information theory, control systems theory, neural networks manifolds, etc. It has potential ability to be applied to general disciplines including physical and engineering sciences.
収録刊行物
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- 応用数理
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応用数理 2 (1), 37-56, 1992
一般社団法人 日本応用数理学会
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詳細情報 詳細情報について
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- CRID
- 1390001205766419456
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- NII論文ID
- 110007390345
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- NII書誌ID
- AN10288886
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- ISSN
- 24321982
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- 本文言語コード
- ja
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- データソース種別
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- JaLC
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可
