You are currently offline. >> stream �Gt�G-�~�.�݊�)r�^��� }�]l�3�,�i�.XC��_% ʏA����?��~v��Y֔*����$���})��4:�\m�w&�Mb����N]�����靸�epɚG�S���Л!��� !�-��oUG�3`�g�&��F��� ��0���Hc��|9���Z�ˍ���� y��:u���m)KhA�/�2z�����v�X��-��Z��0�ҏ�����*`�V�o�G�u��|�-`��yy��ȩ����pe(m�9�#�d�����g�u�qm)�>���ˢx�����%yW�e�w RN-�$7.�K��{l�k[S���B�"�+��6�V~�]`g���Ƥs[ӭ��(���E�M�f�.���D���k�%J_E�$�����=�����Nl�T�և4 �B�q�9FW��=���yu���d*�L�ε��6�ѣ�єvJ;��S9@�$����)%M%��*ߎO2fBi���fX�P�ǀ���B�7ʚ?��v�lc����"�땉�5��ve�P��u�+!�)&��G�+Z����-�����ҿ3�y렯�D9=� W�ÿ:0�"���_{T��C�޷ �EAc_�{d�MhTKl5����;�K�+��6�7���Y�oK������ͪ����� �"�#+. /Contents 4 0 R endobj /FontDescriptor 6 0 R %���� /XObject << 2 0 obj /Widths 30 0 R /Image14 14 0 R /FirstChar 32 14 0 obj Statistical manifolds (M;g;C) 4. /Type /Group /Filter /FlateDecode /LastChar 176 1061 0 obj <> endobj /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 Semantic Scholar is a free, AI-powered research tool for scientific literature, based at the Allen Institute for AI. h޼V�Sgwِ �]�P4م0JJ�P��d��z�� h)���:�$��K{Z�0%`�Qo���v� P�9���S��nX,~�Û��{�w��;�����y?��}v� � �͂P �n@��AA` g�. /Image9 9 0 R endobj << /F2 12 0 R 5 0 obj 15 0 obj endobj >> >> >> Institute for Gravitational Physics and Geometry Physics Department, Penn State, University Park, PA 16802-6300 2. /CS /DeviceRGB /Encoding /WinAnsiEncoding >> >> The Introduction by R.E. >> The exposition is self-contained by concisely introducing the necessary concepts of differential geometry, but proofs … >> /F1 5 0 R << /Group << @����R;������;Y�F��ٸ`�) /GS7 7 0 R /Length 336 endstream << The present work introduces some of the basics of information geometry with an eye on ap-plications in … 4 0 obj 0 Download PDF Abstract: In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. /Image20 20 0 R /Subtype /TrueType Information geometry for neural networks Daniel Wagenaar 6th April 1998 Information geometry is the result of applying non-Euclidean geometry to probability theory. L��R9љ��U ��"O6��bw?��0-�$+چ�.����zf�```nݪ+�zO����^�ka9y4Z��ܘ236�K�.�XI:{�{��)%���{�(���:T�q� ����8�t�?��[��g'.t]�ֻDu��i��U���C /Type /XObject PDF | This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. %%EOF /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 <>/Filter/FlateDecode/ID[<670E018443DC9E1FFF46DB976471141E><20D3F3E192798449BD986F0F1099562B>]/Index[1061 49]/Info 1060 0 R/Length 104/Prev 1063445/Root 1062 0 R/Size 1110/Type/XRef/W[1 2 1]>>stream 1109 0 obj <>stream /Count 1 /Type /Font /BitsPerComponent 8 Name Date GEOMETRY QUICK GUIDE 1: ANGLES Angle Types Angle Rules a So a + b + c = 180° Angles in a triangle add up to 180° Angles on a straight line add endstream endobj startxref endstream /Width 241 /Subtype /Image >> /Image17 17 0 R h�bbd``b���w�� �6ĭL� �QqH0� �� V:�� b 1�!d�H�e�Q� ��{H�M��Y@v000���� OYm >> /Height 102