Methods of Information Geometry
Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.
Elementary differential geometry
The geometric structure of statistical models
Statistical inference and differential geometry
The geometry of time series and linear systems
Multiterminal information theory and statistical inference
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a-connections addition Amari applied arbitrary assume asymptotically components condition connection consider consisting constant contained convex coordinate system corresponding covariance curvature curve defined definition denote derivative determined differential geometry direction discussion divergence dual dualistic structure dually flat element Equation equivalent error estimation theory Example exists exponential family expressed finite Fisher information Fisher metric function given hence holds induced inference information geometry inner product introduced invariant linear manifold mapping Mathematics matrix mean measurement natural necessary normal Note observed obtain operator orthogonal parallel parameter particular positive possible probability distributions problem properties quantum relation represented respect result Riemannian satisfies simply space statistical model structure submanifold sufficient suppose symmetric tangent space tangent vector tensor Theorem theory tion transformation translation vector fields written
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Advances in Neural Information Processing Systems 17: Proceedings of the ...
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Visualização parcial - 2005