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Paper Abstract and Keywords
Presentation 2025-01-29 10:45
Improvement of SPAR-SINK, a Sparsification Method for the Sinkhorn Algorithm
Naoki Ito, Kira Maeda, Yu Nishiyama (UEC) NC2024-53
Abstract (in Japanese) (See Japanese page) 
(in English) The Sinkhorn algorithm enables solving the entropic optimal transport problem with a computational cost of $O(n^2)$ per iteration. However, for practical applications, further reduction in computational cost is essential. As one approach, textsc{Spar-Sink} (M. Li et al., JMLR 2023) introduces stochastic sparsification of the Gibbs kernel matrix, reducing the complexity of each iteration to $O(mathrm{nnz})$, where $mathrm{nnz}$ denotes the number of non-zero entries in the sparsified kernel matrix which is smaller order than $O(n^2)$. Despite its computational efficiency, this method appears to underutilize its potential approximation capacity, as it primarily focuses on the input and target transport measures while neglecting the intrinsic structure of the approximated matrix itself. In this study, we propose an improvement by incorporating the information of the original Gibbs kernel matrix into its stochastic approximation. Specifically, we generalize the sparsification process by introducing an exponent hyperparameter that adjusts the sparsification mechanism. Numerical experiments demonstrate that the proposed method achieves superior stability and enhanced precision compared to textsc{Spar-Sink}. Furthermore, we observed additional improvements in performance when experimenting with different values of the exponent hyperparameter.
Keyword (in Japanese) (See Japanese page) 
(in English) optimal transport / entropic optimal transport / Sinkhorn algorithm / textsc{Spar-Sink} / sparsification / / /  
Reference Info. IEICE Tech. Rep., vol. 124, no. 363, NC2024-53, pp. 66-71, Jan. 2025.
Paper # NC2024-53 
Date of Issue 2025-01-21 (NC) 
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 NC2024-53

Conference Information
Committee NC NLP  
Conference Date 2025-01-28 - 2025-01-29 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English) NC, NLP, General 
Paper Information
Registration To NC 
Conference Code 2025-01-NC-NLP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Improvement of SPAR-SINK, a Sparsification Method for the Sinkhorn Algorithm 
Sub Title (in English)  
Keyword(1) optimal transport  
Keyword(2) entropic optimal transport  
Keyword(3) Sinkhorn algorithm  
Keyword(4) textsc{Spar-Sink}  
Keyword(5) sparsification  
Keyword(6)  
Keyword(7)  
Keyword(8)  
1st Author's Name Naoki Ito  
1st Author's Affiliation The University of Electro-Communications (UEC)
2nd Author's Name Kira Maeda  
2nd Author's Affiliation The University of Electro-Communications (UEC)
3rd Author's Name Yu Nishiyama  
3rd Author's Affiliation The University of Electro-Communications (UEC)
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Speaker Author-1 
Date Time 2025-01-29 10:45:00 
Presentation Time 25 minutes 
Registration for NC 
Paper # NC2024-53 
Volume (vol) vol.124 
Number (no) no.363 
Page pp.66-71 
#Pages 6 
Date of Issue 2025-01-21 (NC) 

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