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| Presentation | 2010-11-04 15:00 [Poster Presentation] A Unified Framework of Density Ratio Estimation under Bregman Divergence Masashi Sugiyama (Tokyo Inst. of Tech.), Taiji Suzuki (Univ. of Tokyo), Takafumi Kanamori (Nagoya Univ.)  IBISML2010-64 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | Estimation of the ratio of probability densities has attracted a great deal of attention since it can be used for addressing various statistical paradigms such as non-stationarity adaptation, two-sample test, outlier detection, mutual information estimation, dimensionality reduction, independent component analysis, causal inference, conditional density estimation, and probabilistic classification. A naive approach to density ratio approximation is to first estimates numerator and denominator densities separately and then take their ratio. However, this two-step approach does not perform well in practice, and methods for directly estimating the density ratio without going through density estimation have been explored, including methods based on moment matching, probabilistic classification, density matching, and density-ratio fitting. The contributions of this paper are three folds: First, we give a comprehensive review of existing density ratio estimation methods and discuss their pros and cons. The second contribution is that we propose a new framework of density ratio estimation in which a density-ratio model is fitted to the true density-ratio under the Bregman divergence. Our new framework includes all the above existing approaches as special cases, and is substantially more general. Thus, it provides a unified view of various density ratio estimation methods. Finally, we develop a robust density ratio estimation method under the power divergence, which is a novel instance in our framework. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | density ratio / Bregman divergence / logistic regression / kernel mean matching / Kullback-Leibler importance estimation procedure / least-squares importance fitting / / | |
| Reference Info. | IEICE Tech. Rep., vol. 110, no. 265, IBISML2010-64, pp. 33-44, Nov. 2010. | |
| Paper # | IBISML2010-64 | |
| 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 | IBISML2010-64 |
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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 | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A Unified Framework of Density Ratio Estimation under Bregman Divergence |
| Sub Title (in English) | |
| Keyword(1) | density ratio |
| Keyword(2) | Bregman divergence |
| Keyword(3) | logistic regression |
| Keyword(4) | kernel mean matching |
| Keyword(5) | Kullback-Leibler importance estimation procedure |
| Keyword(6) | least-squares importance fitting |
| Keyword(7) | |
| Keyword(8) | |
| 1st Author's Name | Masashi Sugiyama |
| 1st Author's Affiliation | Tokyo Institute of Technology (Tokyo Inst. of Tech.) |
| 2nd Author's Name | Taiji Suzuki |
| 2nd Author's Affiliation | University of Tokyo (Univ. of Tokyo) |
| 3rd Author's Name | Takafumi Kanamori |
| 3rd Author's Affiliation | Nagoya University (Nagoya Univ.) |
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| Speaker | Author-1 |
| Date Time | 2010-11-04 15:00:00 |
| Presentation Time | 180 minutes |
| Registration for | IBISML |
| Paper # | IBISML2010-64 |
| Volume (vol) | vol.110 |
| Number (no) | no.265 |
| Page | pp.33-44 |
| #Pages | 12 |
| Date of Issue | 2010-10-28 (IBISML) |
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