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Paper Abstract and Keywords
Presentation 2015-03-05 14:15
Bayes Projection of Conditional Normalized Maximum Likelihood Distributions in Poisson Model and Linear Regression Model
Mutsuki Kojima, Fumiyasu Komaki (UT) IBISML2014-86
Abstract (in Japanese) (See Japanese page) 
(in English) In the Poisson model and the linear regression model, we reveal the relations between the conditional normalized maximum likelihood (CNML) distributions and Bayesian predictive densities based on the latent information priors (LIPs).
In particular, CNML3, which is one type of CNML distributions, is investigated.
The Bayes projection of a predictive density is an information projection of the predictive density on a set of Bayesian predictive densities.
For the Poisson model, we numerically verify that the Bayes projection of CNML3 is asymptotically identical to the Bayesian predictive density based on LIP.
In addition, for the linear regression model, we prove that the Bayes projection of CNML3 coincides with the Bayesian predictive density based on LIP.
Keyword (in Japanese) (See Japanese page) 
(in English) conditional mutual information / Kullback--Leibler divergence / latent information prior / least favorable prior / minimax predictive density / regret / Renyi divergence /  
Reference Info. IEICE Tech. Rep., vol. 114, no. 502, IBISML2014-86, pp. 9-15, March 2015.
Paper # IBISML2014-86 
Date of Issue 2015-02-26 (IBISML) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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 IBISML  
Conference Date 2015-03-05 - 2015-03-06 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyoto University 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Statistical mathematics, machine learning, data mining, and others 
Paper Information
Registration To IBISML 
Conference Code 2015-03-IBISML 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Bayes Projection of Conditional Normalized Maximum Likelihood Distributions in Poisson Model and Linear Regression Model 
Sub Title (in English)  
Keyword(1) conditional mutual information  
Keyword(2) Kullback--Leibler divergence  
Keyword(3) latent information prior  
Keyword(4) least favorable prior  
Keyword(5) minimax predictive density  
Keyword(6) regret  
Keyword(7) Renyi divergence  
1st Author's Name Mutsuki Kojima  
1st Author's Affiliation The University of Tokyo (UT)
2nd Author's Name Fumiyasu Komaki  
2nd Author's Affiliation The University of Tokyo (UT)
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Date Time 2015-03-05 14:15:00 
Presentation Time 30 
Registration for IBISML 
Paper # IEICE-IBISML2014-86 
Volume (vol) IEICE-114 
Number (no) no.502 
Page pp.9-15 
#Pages IEICE-7 
Date of Issue IEICE-IBISML-2015-02-26 

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