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Paper Abstract and Keywords
Presentation 2015-09-14 13:00
On the statistical properties and parametrization of curved exponential families -- from the view point of $tau$-information geometry --
Masaru Tanaka (Fukuoka Univ.) PRMU2015-69 IBISML2015-29
Abstract (in Japanese) (See Japanese page) 
(in English) For curved exponential family, its statistical properties depend on a parameterization. In 1982, Hougaard gives single differential equation with one parameter $delta$ in order to make the dependency of statistical properties on the parameterization clear. Then, in 1984, Kass shows that the Hougaard's differential equation is equivalent to the $alpha$-connection with respect to the new transformed parameter, and the parameter included the Hougaard differential equation is related to the $alpha$ parameter such as $alpha = 1 - 2 delta$. In 1999, Ellem extended the result of Kass to multidimensional case to investigate generalized linear models. They are all shown in the context of Amari's information geometry. But there is another type of information geometry called $tau$-information geometry. In this paper, it is shown that the Ellem's result still hold in the context of $tau$-information geometry.
Keyword (in Japanese) (See Japanese page) 
(in English) curved exponential family / $alpha$-connection / connection condition / $alpha$-affine conjugate / contraction / $tau$-log-likelihood / /  
Reference Info. IEICE Tech. Rep., vol. 115, no. 224, PRMU2015-69, pp. 13-18, Sept. 2015.
Paper # PRMU2015-69 
Date of Issue 2015-09-07 (PRMU, 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. (No. 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee PRMU IBISML IPSJ-CVIM  
Conference Date 2015-09-14 - 2015-09-15 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
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Paper Information
Registration To PRMU 
Conference Code 2015-09-PRMU-IBISML-CVIM 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) On the statistical properties and parametrization of curved exponential families 
Sub Title (in English) from the view point of $tau$-information geometry 
Keyword(1) curved exponential family  
Keyword(2) $alpha$-connection  
Keyword(3) connection condition  
Keyword(4) $alpha$-affine conjugate  
Keyword(5) contraction  
Keyword(6) $tau$-log-likelihood  
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1st Author's Name Masaru Tanaka  
1st Author's Affiliation Fukuoka University (Fukuoka Univ.)
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Speaker
Date Time 2015-09-14 13:00:00 
Presentation Time 30 
Registration for PRMU 
Paper # IEICE-PRMU2015-69,IEICE-IBISML2015-29 
Volume (vol) IEICE-115 
Number (no) no.224(PRMU), no.225(IBISML) 
Page pp.13-18 
#Pages IEICE-6 
Date of Issue IEICE-PRMU-2015-09-07,IEICE-IBISML-2015-09-07 


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