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| Presentation | 2022-12-23 15:10 Fixed Support Tree-Sliced Wasserstein Barycenter Yuki Takezawa, Ryoma Sato (Kyoto Univ./RIKEN AIP), Zornitsa Kozareva (Meta AI), Sujith Ravi (SliceX AI), Makoto Yamada (Kyoto University/RIKEN AIP/OIST)  IBISML2022-63 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The Wasserstein barycenter has been widely studied in various fields, including natural language processing, and computer vision. However, it requires a high computational cost to solve the Wasserstein barycenter problem because the computation of the Wasserstein distance requires a quadratic time with respect to the number of supports. By contrast, the Wasserstein distance on a tree, called the tree-Wasserstein distance, can be computed in linear time and allows for the fast comparison of a large number of distributions. In this study, we propose a barycenter under the tree-Wasserstein distance, called the fixed support tree-Wasserstein barycenter (FS-TWB) and its extension, called the fixed support tree-sliced Wasserstein barycenter (FS-TSWB). More specifically, we first show that the FS-TWB and FS-TSWB problems are convex optimization problems and can be solved by using the projected subgradient descent. Moreover, we propose a more efficient algorithm to compute the subgradient and objective function value by using the properties of tree-Wasserstein barycenter problems. Through real-world experiments, we show that, by using the proposed algorithm, the FS-TWB and FS-TSWB can be solved two orders of magnitude faster than the original Wasserstein barycenter. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Wasserstein Distance / Wasserstein Barycenter / Optimal Transport / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 122, no. 325, IBISML2022-63, pp. 142-149, Dec. 2022. | |
| Paper # | IBISML2022-63 | |
| Date of Issue | 2022-12-15 (IBISML) | |
| ISSN | 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 | IBISML2022-63 |
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| Conference Information | |
| Committee | IBISML |
| Conference Date | 2022-12-22 - 2022-12-23 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kyoto University |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Machine Learning, etc. |
| Paper Information | |
| Registration To | IBISML |
| Conference Code | 2022-12-IBISML |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Fixed Support Tree-Sliced Wasserstein Barycenter |
| Sub Title (in English) | |
| Keyword(1) | Wasserstein Distance |
| Keyword(2) | Wasserstein Barycenter |
| Keyword(3) | Optimal Transport |
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| 1st Author's Name | Yuki Takezawa |
| 1st Author's Affiliation | Kyoto University/RIKEN AIP (Kyoto Univ./RIKEN AIP) |
| 2nd Author's Name | Ryoma Sato |
| 2nd Author's Affiliation | Kyoto University/RIKEN AIP (Kyoto Univ./RIKEN AIP) |
| 3rd Author's Name | Zornitsa Kozareva |
| 3rd Author's Affiliation | Meta AI (Meta AI) |
| 4th Author's Name | Sujith Ravi |
| 4th Author's Affiliation | SliceX AI (SliceX AI) |
| 5th Author's Name | Makoto Yamada |
| 5th Author's Affiliation | Kyoto University/RIKEN AIP/OIST (Kyoto University/RIKEN AIP/OIST) |
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| Speaker | Author-1 |
| Date Time | 2022-12-23 15:10:00 |
| Presentation Time | 20 minutes |
| Registration for | IBISML |
| Paper # | IBISML2022-63 |
| Volume (vol) | vol.122 |
| Number (no) | no.325 |
| Page | pp.142-149 |
| #Pages | 8 |
| Date of Issue | 2022-12-15 (IBISML) |
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