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Paper Abstract and Keywords
Presentation 2010-03-05 14:40
Redundancy analysis of the universal source code with a singular prior
Tatsuya Hashimoto, Tsutomu Kawabata (Univ. of Electro-Comm.) IT2009-125 ISEC2009-133 WBS2009-104
Abstract (in Japanese) (See Japanese page) 
(in English) We consider the universal source coding with the class of source whose probability is parameterized over a continuous space by $theta$. Under a regularity condition, the code length minus the maximum likelihood is proportional to the half logarithm of the data length $n$. It is widely argued that the proportional coefficient is the dimension of the parameter space. Takahashi assumed a singular prior and showed that the proportional coefficient can be bounded from above by the sum of the Hausdorff dimension of each scalar coordinate. In this paper we improve Takahashi's result in two-fold. One is that we extend the type of prior to the one for which Takahashi's coefficient is not tight even after a rotation, and improve his upper bound. The second, we assume for the prior the $text{stationary}^{*}$ and $text{ergodic}^{*}$ measure on self-similar set, and improve the upper bound from the Hausdorff dimension to the tighter effective dimension (R'enyi entropy).
Keyword (in Japanese) (See Japanese page) 
(in English) Hausdorff dimension / universal source cording / redundancy / prior / effective dimension / / /  
Reference Info. IEICE Tech. Rep., vol. 109, no. 444, IT2009-125, pp. 349-352, March 2010.
Paper # IT2009-125 
Date of Issue 2010-02-25 (IT, ISEC, WBS) 
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 IT2009-125 ISEC2009-133 WBS2009-104

Conference Information
Committee IT ISEC WBS  
Conference Date 2010-03-04 - 2010-03-05 
Place (in Japanese) (See Japanese page) 
Place (in English) Nagano-Engineering Campus, Shinshu University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To IT 
Conference Code 2010-03-IT-ISEC-WBS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Redundancy analysis of the universal source code with a singular prior 
Sub Title (in English)  
Keyword(1) Hausdorff dimension  
Keyword(2) universal source cording  
Keyword(3) redundancy  
Keyword(4) prior  
Keyword(5) effective dimension  
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1st Author's Name Tatsuya Hashimoto  
1st Author's Affiliation University of Electro-Communications (Univ. of Electro-Comm.)
2nd Author's Name Tsutomu Kawabata  
2nd Author's Affiliation University of Electro-Communications (Univ. of Electro-Comm.)
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Speaker Author-1 
Date Time 2010-03-05 14:40:00 
Presentation Time 25 minutes 
Registration for IT 
Paper # IT2009-125, ISEC2009-133, WBS2009-104 
Volume (vol) vol.109 
Number (no) no.444(IT), no.445(ISEC), no.446(WBS) 
Page pp.349-352 
#Pages 4 
Date of Issue 2010-02-25 (IT, ISEC, WBS) 

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