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/MediaBox [0 0 612 792] /ViewerPreferences 35 0 R Hoza_ 69, 00-681 Warszawa, Poland November 17, 2005 Related Articles It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the $\alpha$-connections. stream << /ExtGState << /Lang (I��K? the fundamental theorem in information geometry 3. /Tabs /S endobj /Font << /S /Transparency /Image23 23 0 R << Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul. /Interpolate false << Some features of the site may not work correctly. QUANTUM GEOMETRY AND ITS APPLICATIONS Abhay Ashtekar1 and Jerzy Lewandowski2 1. �#��D ��,?�����π�nZ�-���nhVq�4�}����F�|�O�_��0�nOqw��9%�mF����- �J=�q��Qa��[���X-v6�T$�^hizy�Nqg"���kUO�H.�8�%1o1�a˷�����_�&E1���s�. Examples of dually metric-coupled connection geometry: A. Dual geometry induced by a divergence B. Dually flat Pythagorean geometry (from Bregman divergences) C. Expected -geometry (from invariant statistical f … ��M#��vnU���v:q%.�ҔuizA����P�=�1������1k"�G͚�: �z����*�TG��~���$����o/��@� ��|/x�X���� c�Zm�
���)A#-���^|�lY�>�(2m�� �b A new class of entropic information measures, formal group theory and information geometry, Classification and Discrimination in Models for Ordered Data, Correlation and Independence in the Neural Code, Cram\'er-Rao Lower Bounds Arising from Generalized Csisz\'ar Divergences, Cramér-Rao Lower Bounds Arising from Generalized Csiszár Divergences, Curvature based triangulation of metric measure spaces, Discrete versions of the transport equation and the Shepp--Olkin conjecture, Distribution-free Evolvability of Vector Spaces: All it takes is a Generating Set, Inference on the eigenvalues of the covariance matrix of a multivariate normal distribution—Geometrical view, Infinite-dimensional statistical manifolds based on a balanced chart, View 32 excerpts, cites background and methods, View 6 excerpts, cites background and methods, View 5 excerpts, cites background and methods, View 9 excerpts, cites background and methods, By clicking accept or continuing to use the site, you agree to the terms outlined in our. /Kids [3 0 R] %PDF-1.7 /Pages 2 0 R
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Download PDF Abstract: In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. /Image20 20 0 R /Subtype /TrueType Information geometry for neural networks Daniel Wagenaar 6th April 1998 Information geometry is the result of applying non-Euclidean geometry to probability theory. L��R9љ��U
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/Image10 10 0 R Methods of information geometry @inproceedings{Amari2000MethodsOI, title={Methods of information geometry}, author={S. Amari and H. Nagaoka}, year={2000} } /SMask 16 0 R DOI: 10.1090/mmono/191 Corpus ID: 116976027. 1083 0 obj
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