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 |
Copyright and reproduction |
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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MI2013-32 |
Conference Information |
Committee |
MI |
Conference Date |
2013-07-18 - 2013-07-19 |
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(See Japanese page) |
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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) |
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Keyword(1) |
Information geometry |
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Hessian geometry |
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Tsallis statistics |
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Estimating function |
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Divergence |
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Hiroshi Matsuzoe |
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Nagoya Institute of Technology (NIT) |
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Speaker |
Author-1 |
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 |
1 |
Date of Issue |
2013-07-11 (MI) |
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