Information Geometry and its Applications III

Abstract Shinto Eguchi

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Shinto Eguchi  (Institute of Statistical Mathematics, Japan)
Monday, August 02, 2010, room Hörsaal 1
U-entropy and maximum entropy model

Boltzmann-Shannon entropy leads to an exponential model as the maximum entropy model with the constraint to the space of pdfs under which expectations of a given statistic t(x) become a common vector. The maximum likelihood estimator for the expectation parameter of t(x) under the exponential model is characterized by specific properties such as the attainment the Cramer-Rao bound. Any generator function U defines U-entropy and U-divergence from the assumption of convexity of U. In this framework, U-entropy leads to U-model as the maximum entropy model under which the minimum U-divergence estimator for the expectation parameter is characterized by a structure of orthogonal foliation. If formula21, then this reduces to the case of Boltzmann-Shannon entropy. Surprisingly, we observe that the minimum U-divergence estimator under the U-model has a unique form, that is, the sample mean of t(x). Alternatively if the minimum U-divergence estimator is employed under another U-model, then the estimator has a different form with the weighted mean of t(x) over the sample. This talk discusses information geometric understandings for this aspect with Pythagoras identity, minimax game and robustness.


Date and Location

August 02 - 06, 2010
University of Leipzig
04103 Leipzig

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
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František Matúš
Academy of Sciences of the Czech Republic
Institute of Information Theory and Automation
Czech Republic
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Scientific Committee

Shun-ichi Amari
Brain Science Institute, Mathematical Neuroscience Laboratory
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
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Administrative Contact

Antje Vandenberg
Max Planck Institute for Mathematics in the Sciences
Contact by Email
Phone: (++49)-(0)341-9959-552
Fax: (++49)-(0)341-9959-555

05.04.2017, 12:42