40 0 0 0 OA 情報幾何学

著者
甘利 俊一
出版者
一般社団法人 日本応用数理学会
雑誌
応用数理 (ISSN:24321982)
巻号頁・発行日
vol.2, no.1, pp.37-56, 1992-03-16 (Released:2017-04-08)
参考文献数
26

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.

10 0 0 0 OA 情報幾何学

著者
甘利 俊一
出版者
一般社団法人日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.2, no.1, pp.37-56, 1992-03-16
被引用文献数
3 or 0

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.
著者
甘利 俊一 尾関 智子 朴 慧暎
出版者
日本神経回路学会
雑誌
日本神経回路学会誌 (ISSN:1340766X)
巻号頁・発行日
vol.10, no.4, pp.189-200, 2003-12-05 (Released:2011-03-14)
参考文献数
40
被引用文献数
2 or 0

多層パーセプトロンなどの神経回路網の全体を多様体として幾何学的に考察するとき, ここには階層構造に由来する特異点が本質的に含まれることがわかる. これには, 学習の遅滞, 精度の劣化など, 実際の多くの問題が関係している. 本稿は, 主に日本で発展している, 特異構造を含むモデルの統計的推論と学習のダイナミックスを取り扱い, その考え方を示し, 現在までに著者らが得ている研究の成果と構想について解説する.
著者
甘利俊一 [ほか] 編集
出版者
岩波書店
巻号頁・発行日
1993

1 0 0 0 OA 人工知能

著者
南雲 仁一 甘利 俊一 中野 馨
出版者
公益社団法人 計測自動制御学会
雑誌
計測と制御 (ISSN:04534662)
巻号頁・発行日
vol.11, no.1, pp.58-68, 1972 (Released:2009-11-26)
参考文献数
76
被引用文献数
1 or 0
著者
甘利 俊一 藤原 祐介
出版者
物性研究刊行会
雑誌
物性研究 (ISSN:07272997)
巻号頁・発行日
vol.87, no.3, pp.457-466, 2006-12-20

この論文は国立情報学研究所の電子図書館事業により電子化されました。
著者
甘利 俊一 川鍋 元明
出版者
一般社団法人日本応用数理学会
雑誌
応用数理 (ISSN:09172270)
巻号頁・発行日
vol.6, no.2, pp.96-109, 1996-06-17
被引用文献数
10 or 0

The present paper studies estimation of the coefficient θ of a linear dependence relation y=θx between two variables x and y from n pairs (y_i, x_i), i=1, …, n, of noise-contaminated observations. This is an old problem where the maximum likelihood estimator or the least square estimator is known not to be a,symptotically optimal. A simple estimator which improves the above one is explicitly given. This is a typical example of semiparametric statistical estimation. The method of estimating functions is used to solve the problem. Information geometry is used for elucidating the set of all the estimating functions and the asymptotic efficiency of the related estimators. A fibre structure is composed on the manifold of a semiparametric model and a dual couple of parallel transports are introduced on the fibres.
著者
甘利 俊一 内田 肇
出版者
物性研究刊行会
雑誌
物性研究 (ISSN:05252997)
巻号頁・発行日
vol.87, no.3, pp.451-456, 2006-12

この論文は国立情報学研究所の電子図書館事業により電子化されました。研究会報告