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Paper Abstract and Keywords
Presentation 2013-07-19 10:40
[Special Talk] Geometry of Statistical Models from the Viewpoint of Differential Geometry
Hiroshi Matsuzoe (NIT) MI2013-32
Abstract (in Japanese) (See Japanese page) 
(in English) In geometric theory of statistical inferences, geometry of parameter spaces of probability distributions is called information geometry. In information geometry, a parametric statistical model is regarded as a Riemannian manifold, and a pair of dualistic affine connections plays an important role. An exponential family is a typical statistical model in statistics, which includes the set of Gaussian distributions. An exponential family has Hessian structures, and these geometric quantities are induced form the Kullback-Leibler divergence.
On the other hand, probability densities of non-exponential type are useful in the theory of complex systems. A deformed exponential family is an example of a set of such probability distributions, and is introduced as a generalization of exponential families. A deformed exponential family naturally has two kinds of Hessian structures. In this presentation, we discuss these geometric structures and explain relations to geometry of divergences.
In addition, from discussions above, we find that notions of expectations and independences for random variables are dependent to the given statistical model. As applications, we consider a generalization of independences and generalize the maximum likelihood methods.
Keyword (in Japanese) (See Japanese page) 
(in English) Information geometry / Hessian geometry / Tsallis statistics / Estimating function / Divergence / / /  
Reference Info. IEICE Tech. Rep., vol. 113, no. 146, MI2013-32, pp. 67-67, July 2013.
Paper # MI2013-32 
Date of Issue 2013-07-11 (MI) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
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All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee MI  
Conference Date 2013-07-18 - 2013-07-19 
Place (in Japanese) (See Japanese page) 
Place (in English)  
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Paper Information
Registration To MI 
Conference Code 2013-07-MI 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Geometry of Statistical Models from the Viewpoint of Differential Geometry 
Sub Title (in English)  
Keyword(1) Information geometry  
Keyword(2) Hessian geometry  
Keyword(3) Tsallis statistics  
Keyword(4) Estimating function  
Keyword(5) Divergence  
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1st Author's Name Hiroshi Matsuzoe  
1st Author's Affiliation Nagoya Institute of Technology (NIT)
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Date Time 2013-07-19 10:40:00 
Presentation Time 60 minutes 
Registration for MI 
Paper # MI2013-32 
Volume (vol) vol.113 
Number (no) no.146 
Page p.67 
#Pages
Date of Issue 2013-07-11 (MI) 


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