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| Presentation | 2010-11-04 15:00 [Poster Presentation] Boosting for density estimation based on U loss function Osamu Komori (ISM), Kanta Naito (S.U.), Shinto Eguchi (ISM)  IBISML2010-69 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | In this paper, we propose a class of methods for density estimation by boosting technique. By the iterative minimization of the $U$ loss function, which derives from a monotonically increasing convex function, we consider a boosting algorithm for the unsupervised learning. In the boosting algorithm, the weak learners in a predetermined set of density functions are combined convexly to produce an optimal density estimator. We want to choose the best $U$ function in the setting above. If we consider $U$ as $\beta$ power function, then the $U$ loss function is equivalent to the $L_2$ norm; moreover, we find see that the $U$ loss function approaches the negative likelihood as $\beta$ goes to 0. Hence, our proposed method is very general in these respects. We clarify that the proposed algorithm includes a penalty term that prevents over-learning or overfitting to the data, by investigating the updated $U$ loss function that can be divided into two parts. Furthermore, we derive a formula that shows a non-asymptotic bound for the density estimator. Finally, we demonstrate the utility of our method by simulation studies. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Divergence / Boosting / Density estimation / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 110, no. 265, IBISML2010-69, pp. 73-82, Nov. 2010. | |
| Paper # | IBISML2010-69 | |
| Date of Issue | 2010-10-28 (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 | IBISML2010-69 |
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| Conference Information | |
| Committee | IBISML |
| Conference Date | 2010-11-04 - 2010-11-06 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | IIS, Univ. of Tokyo |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | IBIS 2010 (Workshop on Information-based Induction Sciences) |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2010-11-IBISML |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Boosting for density estimation based on U loss function |
| Sub Title (in English) | |
| Keyword(1) | Divergence |
| Keyword(2) | Boosting |
| Keyword(3) | Density estimation |
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| 1st Author's Name | Osamu Komori |
| 1st Author's Affiliation | The Institute of Statistical Mathematics (ISM) |
| 2nd Author's Name | Kanta Naito |
| 2nd Author's Affiliation | Shimane University (S.U.) |
| 3rd Author's Name | Shinto Eguchi |
| 3rd Author's Affiliation | Shimane University (ISM) |
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| Speaker | Author-1 |
| Date Time | 2010-11-04 15:00:00 |
| Presentation Time | 180 minutes |
| Registration for | IBISML |
| Paper # | IBISML2010-69 |
| Volume (vol) | vol.110 |
| Number (no) | no.265 |
| Page | pp.73-82 |
| #Pages | 10 |
| Date of Issue | 2010-10-28 (IBISML) |
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