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Titlebook: Geometric Structures of Information; Frank Nielsen Book 2019 Springer Nature Switzerland AG 2019 Hessian Information Geometry.Shape Space.

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Information-Theoretic Matrix Inequalities and Diffusion Processes on Unimodular Lie Groups,ifically, they have the properties of shift-invariant integration, an associative convolution operator, well-defined diffusion processes, and concepts of Entropy, Fisher information, Gaussian distribution, and Fourier transform. Equipped with these definitions, it is shown that many inequalities fro
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Warped Riemannian Metrics for Location-Scale Models,lso of fundamental importance in information geometry. Precisely, the starting point is a new theorem, which states that the Rao–Fisher information metric of any location-scale model, defined on a Riemannian manifold, is a warped Riemannian metric, whenever this model is invariant under the action o
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Timothy D. Brewerton,Kathleen Bradypass this problem, we consider performing stochastic Monte Carlo (MC) estimation of those integral-based mixture/exponential family Bregman generators. We show that, under natural assumptions, these MC generators are almost surely Bregman generators. We define a series of dually flat information geo
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Anisotrope Scheiben und Platten,ect of considerably under-estimating standard errors when compared to our more general assumptions and, potentially, introducing bias. We comment on the implications of this. The survival times of adult acute myeloid leukaemia patients in northwest England are analyzed.
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