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| Presentation | 2014-11-18 15:00 [Poster Presentation] Gauge Theory on Measure Space -- tau-Information Geometry -- Masaru Tanaka (Fukuoka Univ.)  IBISML2014-72 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | A new formulation of information geometry is given by extending a translation operation on an affine space of probability density functions with up to scale from a logarithmic function to a $tau$-logarithmic function. In this formulation, this extended translation is called a $tau$-affine structure and an affine space with a $tau$-affine structure is called a $tau$-affine space. Its dual space is defined by taking a H"{o}lder conjugation. A contraction operation is defined on a $tau$-affine space and its conjugated space. This leads to Fisher metric for score functions. Then it is revealed that Fisher metric is independent of a $tau$-affine structure. The definition of an entropy requires a renormalization process. With a renormalization technique for a $tau$-log-likelihood, the contraction leads to a new definition of an expectation. This new expectation reveals that an escort distribution is nothing but a normalized and renormalized $tau$-log-likelihood. Therefore, the escort distribution is no longer necessary for us. By using this new expectation, a conformal entropy is also given. The conformal entropy is related to Tsallis entropy with a simple modification and gives two types of non-additivity according to formulae of $tau$-logarithmic function for multiplication. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | $tau$-affine structure / contraction / $tau$-log-likelihood / escort distribution / renormalization / entropy / non-additivity / | |
| Reference Info. | IEICE Tech. Rep., vol. 114, no. 306, IBISML2014-72, pp. 279-286, Nov. 2014. | |
| Paper # | IBISML2014-72 | |
| Date of Issue | 2014-11-10 (IBISML) | |
| 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) | |
| Download PDF | IBISML2014-72 |
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| Conference Information | |
| Committee | IBISML |
| Conference Date | 2014-11-17 - 2014-11-19 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Nagoya Univ. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2014-11-IBISML |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Gauge Theory on Measure Space |
| Sub Title (in English) | tau-Information Geometry |
| Keyword(1) | $tau$-affine structure |
| Keyword(2) | contraction |
| Keyword(3) | $tau$-log-likelihood |
| Keyword(4) | escort distribution |
| Keyword(5) | renormalization |
| Keyword(6) | entropy |
| Keyword(7) | non-additivity |
| Keyword(8) | |
| 1st Author's Name | Masaru Tanaka |
| 1st Author's Affiliation | Fukuoka University (Fukuoka Univ.) |
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| Speaker | Author-1 |
| Date Time | 2014-11-18 15:00:00 |
| Presentation Time | 180 minutes |
| Registration for | IBISML |
| Paper # | IBISML2014-72 |
| Volume (vol) | vol.114 |
| Number (no) | no.306 |
| Page | pp.279-286 |
| #Pages | 8 |
| Date of Issue | 2014-11-10 (IBISML) |
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