Information Geometry and its Applications III

Abstract Peter Harremoës

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Peter Harremoës  (Copenhagen Business College, Denmark)
Tuesday, August 03, 2010, room Hörsaal 1
Minimum description length for exponential families

A statistical model is essentially an information channel from a parameter space to a data space so that each parameter gives a distribution over possible data. We are interested in characterizing the statistical models that have finite capacity. According to the Gallager-Ryabko Theorem the capacity equals the minimax redundancy. In the minimum description length (MDL) approach to statistics one is interested in the minimax regret rather than the minimax redundancy of the statistical model. The minimax redundancy lower bounds minimax regret so if capacity is infinite the minimax regret is infinite and the MDL approach to statistics fails. In this talk we shall restrict our attention to exponential families. It has been conjectured that finite capacity implies finite minimax regret. We demonstrate that the conjecture holds in 1 dimension but is violated in 3 dimensions. This is joint work with Peter Grünwald.

Date and Location

August 02 - 06, 2010
University of Leipzig
Augustusplatz
04103 Leipzig
Germany

Scientific Organizers

Nihat Ay
Max Planck Institute for Mathematics in the Sciences
Information Theory of Cognitive Systems Group
Germany
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Paolo Gibilisco
Università degli Studi di Roma "Tor Vergata"
Facoltà di Economia
Italy
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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
RIKEN
Brain Science Institute, Mathematical Neuroscience Laboratory
Japan
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Imre Csiszár
Hungarian Academy of Sciences
Alfréd Rényi Institute of Mathematics
Hungary
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Dénes Petz
Budapest University of Technology and Economics
Department for Mathematical Analysis
Hungary
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Giovanni Pistone
Collegio Carlo Alberto, Moncalieri
Italy
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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