10 0 0 0 OA 情報幾何学

甘利 俊一
応用数理 (ISSN:09172270)
vol.2, no.1, pp.37-56, 1992-03-16

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.


Facebook (1 users, 1 posts)

日本から発信された数理的手法である情報幾何を学ぶための資料。 機械学習などに応用されている。 情報幾何の基礎となる考え方: 情報幾何学 甘利俊一 http://ci.nii.ac.jp/els/110007390345.pdf?id=ART0009255014&type=pdf&lang=jp&host=cinii&order_no=&ppv_type=0&lang_sw=&no=14018836 ...

はてなブックマーク (1 users, 2 posts)

Twitter (8 users, 8 posts, 0 favorites)

甘利先生の解説文、ついに情報幾何に入門できそうな気運ある https://t.co/gRwegbf6Gb
情報幾何学の基礎読んだら寄り道してしまったので甘利先生の資料見て軌道修正する https://t.co/7MqD8Rv0Om
https://t.co/kj1qdplwwa 明日読む
@getjob_kaisyu まぁ、結局は確率分布を各点と考えた多様体論なんですけどね。ちょっと知る程度ならこれですかね? https://t.co/FDTAF3sWy8
情報幾何の基本的スタディ( http://t.co/rSMVU1ZjEG )→情報幾何入門( http://t.co/apcav2JWmO )→情報幾何学( http://t.co/QfGzuXXer3 )の順で読んだけどよかった

収集済み URL リスト