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| Presentation | 2015-06-25 09:30 Online Density Estimation of Bradley-Terry Models Issei Matsumoto (Toyota), Kohei Hatano, Eiji Takimoto (Kyushu U.)  IBISML2015-21 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | We consider an online density estimation problem for Bradley-Terry models that determine the probability of a match result between any pair in a set of $n$ teams. However, in this context, the loss function is not convex. A standard solution to avoid this non-convexity is to change variables such that the new loss function w.r.t.~new variables is convex. However, the radius $K$ of the new domain may then become huge or infinite. When $K$ is considered a constant, standard algorithms OGD and ONS have regret bounds $O(n^{frac{1}{2}}(ln K)sqrt{T})$ and $O(n^{frac{3}{2}}Kln T)$, respectively. We derive a $Theta(T^{n-1})$ bound of the radius $K$ of the reparameterized convex domain under a mild assumption. The bound implies a worst case where the regret bounds of OGD and ONS are $O(n^{frac{3}{2}}sqrt{T}ln T)$ and $tilde{O}(n^{frac{3{2}}(T)^{n-1})$, respectively. We then propose a version of Follow the Regularized Leader, whose regret bound is close to the minimum of those of OGD and ONS. Therefore, the proposed algorithm is competitive both when $K$ is constant or $O(T^{n-1})$. With an appropriate parameter, the proposed algorithm achieves a better regret bound $O(n^{frac{5}{2}}T^{frac{1}{3}} ln T)$ in the worst case. In addition, the proposed algorithm works without knowledge of the radius, which is a practical advantage. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | online density estimation / Bradley-Terry model / ranking / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 115, no. 112, IBISML2015-21, pp. 173-180, June 2015. | |
| Paper # | IBISML2015-21 | |
| Date of Issue | 2015-06-16 (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 | IBISML2015-21 |
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| Conference Information | |
| Committee | NC IPSJ-BIO IBISML IPSJ-MPS |
| Conference Date | 2015-06-23 - 2015-06-25 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Okinawa Institute of Science and Technology |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Machine Learning Approach to Biodata Mining, and General |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2015-06-NC-BIO-IBISML-MPS |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Online Density Estimation of Bradley-Terry Models |
| Sub Title (in English) | |
| Keyword(1) | online density estimation |
| Keyword(2) | Bradley-Terry model |
| Keyword(3) | ranking |
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| 1st Author's Name | Issei Matsumoto |
| 1st Author's Affiliation | Toyota Motor Corporation (Toyota) |
| 2nd Author's Name | Kohei Hatano |
| 2nd Author's Affiliation | Kyushu University (Kyushu U.) |
| 3rd Author's Name | Eiji Takimoto |
| 3rd Author's Affiliation | Kyushu University (Kyushu U.) |
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| Speaker | Author-2 |
| Date Time | 2015-06-25 09:30:00 |
| Presentation Time | 25 minutes |
| Registration for | IBISML |
| Paper # | IBISML2015-21 |
| Volume (vol) | vol.115 |
| Number (no) | no.112 |
| Page | pp.173-180 |
| #Pages | 8 |
| Date of Issue | 2015-06-16 (IBISML) |
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