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| 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 |
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| 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. |
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| 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 | |
| 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 | IBISML2014-86 |
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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 |
| Keyword(8) | |
| 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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| Speaker | Author-1 |
| Date Time | 2015-03-05 14:15:00 |
| Presentation Time | 30 minutes |
| Registration for | IBISML |
| Paper # | IBISML2014-86 |
| Volume (vol) | vol.114 |
| Number (no) | no.502 |
| Page | pp.9-15 |
| #Pages | 7 |
| Date of Issue | 2015-02-26 (IBISML) |
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