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Common terms and phrasesa-connections a-family addition affine connection affine coordinate system Amari arbitrary autoparallel canonical divergence components convex coordinate system corresponding curvature curved exponential family defined denote differential geometry dual connections dualistic structure dually flat space e-curvature efficient estimator embedding encoding entropy Equation equivalent estimating function estimating submanifold Example exponential family finite first-order efficient Fisher information matrix Fisher metric geometric structure given hence induced information geometry information theory inner product invariant Kullback divergence let us consider mapping maximum likelihood estimator measurement mixture family multiterminal mutually dual n-dimensional Nagaoka necessary and sufficient normal distribution Note obtain open subset operator orthogonal parallel translation parameter parameterized probability distributions problem quantum random variable real number Riemannian metric Rn+1 satisfies statistical inference statistical manifolds statistical model stochastic submanifold subspace sufficient statistic suppose symmetric tangent space tangent vector tensor field tion TP(M TP(S transformation unbiased underlying distribution vector fields References to this bookFrom other books
From Google ScholarClustering with Bregman DivergencesArindam Banerjee, Srujana Merugu, Inderjit S Dhillon, Joydeep Ghosh - 2005 - Journal of Machine Learning Research Information Geometry on Hierarchy of Probability DistributionsShun-ichi Amari - 2001 - IEEE TRANSACTIONS ON INFORMATION THEORY Fifty Years of Shannon TheorySergio Verdu - 1998 - IEEE TRANSACTIONS ON INFORMATION THEORY On Quantum Statistical InferenceOle E Barndorff-Nielsen, Richard D Gill, Peter E Jupp - 2003 - Journal of the Royal Statistical Society. Series B, Statistical Methodology References from web pagesInformation geometry - Wikipedia, the free encyclopedia Information Geometry Approach to the Model Selection of Neural ... Information Geometry Stochastic reasoning, free energy, and information geometry citeulike: The geometry of prior selection An Information-Geometric Approach to a Theory of Pragmatic Structuring Information Geometry of α-Projection in Mean Field Approximation ... Blackwell Online - Computers : Machine Theory Phys. Rev. A 70, 012317 (2004): Fujiwara - Estimation of a ... Amabra - Methods of Information Geometry (Tanslations of ... Bibliographic information
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