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Amari S.-I., Nagaoka H. — Methods of Information Geometry
Amari S.-I., Nagaoka H. — Methods of Information Geometry



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Название: Methods of Information Geometry

Авторы: Amari S.-I., Nagaoka H.

Аннотация:

Information geometry, which began as an investigation of the natural differential geometric structure possessed by families of probability distributions, is offered here in a complete treatment, translated from the original 1993 work in Japanese. The topic is applicable to information theory, stochastic processes, and systems, including neurocomputing. The authors, who assume some knowledge of statistics, systems theory and information theory, begin with an introduction to differential geometry and the theory of dual connections, before describing statistical inference, geometry of time series and linear systems, multiterminal information theory and statistical inference, information geometry for quantum systems, concluding with a grab-bag of applications including geometry of convex analysis, linear programming and gradient flows, neuro-manifolds and nonlinear systems, lie groups and transformation models.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 206

Добавлена в каталог: 06.12.2005

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Предметный указатель
$\alpha$-parallel      33
$\nabla$-projection      63
0-rate encoding      135
0-representation      44
Components of a tensor field      9
Conormal vector field      177
Curvature tensor field      18
Efficient test      102
First-order uniformly most powerful test      102
Invariance with respect to a sufficient statistic      38
Modified Pythagorean relation      72 179
Nuisance parameter      109
Nuisance space      112
Nuisance tangent space      111
Observed point      86
Operator convex function      154
parallel      15 17
Parallel translation      15
Parametric model      26
POINTS      1
POM      146
Positive-operator-valued measure      146
Potential of Legendre transformation      60
Power function      101
Power spectrum      116
Principle of maximum entropy      68 125
Probability distributions      25
Probability operator-valued measure      146
Projection of a connection      22
Pure state      146
Pythagorean relation for canonical divergence      62
Quantum $\alpha$-divergence      152
Quantum Cramer — Rao inequality      160 162
Quantum equivalent of the Kullback divergence      152
Quantum f-divergence      151
Quantum measurement      146
Quantum observable      147
Quantum relative entropy      152
Quantum state      145
Quasiclassical      163
Relative entropy      57
Relative modular operator      150
Representation of a tangent vector, $\alpha$-representation      46 153
Representation of a tangent vector, 0-representation      44
Representation of a tangent vector, e-representation, exponential representation      41 155
Representation of a tangent vector, m-representation, mixture representation      40 148
Riemann — Christoffel curvature tensor (field)      18
Riemann — Christoffel curvature tensor field      18
Riemannian connection      24
Riemannian manifold      11
Riemannian metric      11
Sanov's theorem      69 139
Score function      109
Second fundamental form      176
Second-order efficient estimator      96
Simple measurement      147
Single-letterization      143
SLD      156
Stable feedback      127
Stable linear system      116 127
Stable matrix      127
Statistical inference      81
Statistical inference for multiterminal information      133
Statistical manifold      28
Statistical model      25 26 81
Stochastic realization      125
Stochastic realization, $\alpha$-realization      126
Submanifold      10
Sufficient statistic      29 56 86
Symmetric connection      19
Symmetric logarithmic derivative      156
Symmetrized inner product      155
System space      117
Tangent space      5 7
Tangent vector      5 7
Tensor field      8
Tensor field of type (q,r)      8
test      82 100
Time series      115
Torsion tensor (field)      18
Torsion tensor field      18
Torsion-free connection      19
Transfer function      116
Triangular relation      62 77
True distribution      26
Unbiased estimator      31 82
Underlying distribution      26
Uniformly most powerful test      101
Vector field      8
Vector field along a curve      14
von Neumann entropy      153
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