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| Presentation | 2014-02-13 14:00 tau-information geometry: translation on a space of measurable functions Masaru Tanaka (Fukuoka Univ.)  PRMU2013-133 CNR2013-41 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | $tau$-information geometry, that is a new formulation of information geometry, is given by extending a translation operation on an affine space consisting of measurable functions with up to scale. In this formulation, a $tau$-affine space $tilde{P}^{(tau = s)}$ and its $tau$-affine conjugate space $tilde{P}^{(tau = 1 - s)}$ play important roles. $tau$-affine conjugation of a point in $tilde{P}^{(tau = s)}$ gives a point in $tilde{P}^{(tau = 1 - s)}$ with the same affine coordinates. On the $tilde{P}^{(tau = s)} times tilde{P}^{(tau = 1 - s)}$, a contraction, that is an inner product in some sense, is defined. With a renormalization technique for a $tau$-log-likelihood, the contraction leads to a new definition of an expectation. This new expectation admits a usual interpretation, but is essentially different from the usual one. It 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. What we need is the normalized and renormalized $tau$-log-likelihood. It is also given what $alpha$-parameter in $alpha$-dual connections is. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | $tau$-affine structure / $tau$-affine conjugate / contraction / $tau$-log-likelihood / renormalized $tau$-log-likelihood / Fisher metric / / | |
| Reference Info. | IEICE Tech. Rep., vol. 113, no. 431, PRMU2013-133, pp. 67-72, Feb. 2014. | |
| Paper # | PRMU2013-133 | |
| Date of Issue | 2014-02-06 (PRMU, CNR) | |
| 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 | PRMU2013-133 CNR2013-41 |
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| Conference Information | |
| Committee | PRMU CNR |
| Conference Date | 2014-02-13 - 2014-02-14 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | PRMU |
| Conference Code | 2014-02-PRMU-CNR |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | tau-information geometry: translation on a space of measurable functions |
| Sub Title (in English) | |
| Keyword(1) | $tau$-affine structure |
| Keyword(2) | $tau$-affine conjugate |
| Keyword(3) | contraction |
| Keyword(4) | $tau$-log-likelihood |
| Keyword(5) | renormalized $tau$-log-likelihood |
| Keyword(6) | Fisher metric |
| Keyword(7) | |
| 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 | 2014-02-13 14:00:00 |
| Presentation Time | 30 minutes |
| Registration for | PRMU |
| Paper # | PRMU2013-133, CNR2013-41 |
| Volume (vol) | vol.113 |
| Number (no) | no.431(PRMU), no.432(CNR) |
| Page | pp.67-72 |
| #Pages | 6 |
| Date of Issue | 2014-02-06 (PRMU, CNR) |
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