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1.

図書
図書
1. Dynamic interactions in neural networks : models and data (: U.S. ; : Germany)
Michael A. Arbib, Shun-ichi Amari, editors
出版情報: New York ; Tokyo : Springer-Verlag, c1989  viii, 280 p. ; 24 cm
シリーズ名: Research notes in neural computing ; 1
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目次情報:
Development and Learning in Adaptive Networks
Visual Function
Motor Control and the Cerebellum
Development and Learning in Adaptive Networks
Visual Function
Motor Control and the Cerebellum
2.

図書
図書
2. Differential-geometrical methods in statistics (: us ; : gw)
Shun-ichi Amari
出版情報: Berlin ; New York : Springer-Verlag, c1985  v, 290 p. ; 24 cm
シリーズ名: Lecture notes in statistics ; 28
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3.

電子ブック
ＥＢ
3. Differential-geometrical methods in statistics (: electronic bk)
Shun-ichi Amari
出版情報: New York : Springer, [20--]  1 online resource (v, 294 p.)
シリーズ名: Lecture notes in statistics ; 28
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4.

図書
図書
4. Methods of information geometry (: pbk)
Shun-ichi Amari, Hiroshi Nagaoka ; [translated from the Japanese by Daishi Harada]
出版情報: Providence, R.I. : American Mathematical Society , [Oxford] : Oxford University Press, c2000  x, 206 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 191
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目次情報: 続きを見る
Preface
Preface to the English edition
Elementary differential geometry / 1：
Differentiable manifolds / 1.1：
Tangent vectors and tangent spaces / 1.2：
Vector fields and tensor fields / 1.3：
Submanifolds / 1.4：
Riemannian metrics / 1.5：
Affine connections and covariant derivatives / 1.6：
Flatness / 1.7：
Autoparallel submanifolds / 1.8：
Projection of connections and embedding curvature / 1.9：
Riemannian connection / 1.10：
The geometric structure of statistical models / 2：
Statistical models / 2.1：
The Fisher metric / 2.2：
The [alpha]-connection / 2.3：
Chentsov's theorem and some historical remarks / 2.4：
The geometry of P (X) / 2.5：
[alpha]-affine manifolds and [alpha]-families / 2.6：
Dual connections / 3：
Duality of connections / 3.1：
Divergences: general contrast functions / 3.2：
Dually flat spaces / 3.3：
Canonical divergence / 3.4：
The dualistic structure of exponential families / 3.5：
The dualistic structure of [alpha]-affine manifolds and [alpha]-families / 3.6：
Mutually dual foliations / 3.7：
A further look at the triangular relation / 3.8：
Statistical inference and differential geometry / 4：
Estimation based on independent observations / 4.1：
Exponential families and observed points / 4.2：
Curved exponential families / 4.3：
Consistency and first-order efficiency / 4.4：
Higher-order asymptotic theory of estimation / 4.5：
Asymptotics of Fisher information / 4.6：
Higher-order asymptotic theory of tests / 4.7：
The theory of estimating functions and fiber bundles / 4.8：
The fiber bundle of local exponential families / 4.8.1：
Hilbert bundles and estimating functions / 4.8.2：
The geometry of time series and linear systems / 5：
The space of systems and time series / 5.1：
The Fisher metric and the [alpha]-connection on the system space / 5.2：
The geometry of finite-dimensional models / 5.3：
Stable systems and stable feedback / 5.4：
Multiterminal information theory and statistical inference / 6：
Statistical inference for multiterminal information / 6.1：
0-rate testing / 6.2：
0-rate estimation / 6.3：
Inference for general multiterminal information / 6.4：
Information geometry for quantum systems / 7：
The quantum state space / 7.1：
The geometric structure induced from a quantum divergence / 7.2：
The geometric structure induced from a generalized covariance / 7.3：
Applications to quantum estimation theory / 7.4：
Miscellaneous topics / 8：
The geometry of convex analysis, linear programming and gradient flows / 8.1：
Neuro-manifolds and nonlinear systems / 8.2：
Lie groups and transformation models in information geometry / 8.3：
Mathematical problems posed by information geometry / 8.4：
Guide to the Bibliography
Bibliography
Index
Dual connections Statistical inference and differential geometry
Miscellaneous topics Guide to the bibliography
Preface
Preface to the English edition
Elementary differential geometry / 1：
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