2023 Fiscal Year Research-status Report
| Project/Area Number |
22K12175
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| Research Institution | Waseda University |
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Principal Investigator |
笠井 裕之 早稲田大学, 理工学術院, 教授 (40312079)
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| Project Period (FY) |
2022-04-01 – 2025-03-31
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| Keywords | 最適輸送理論 / シンクホーンアルゴリズム / スクリーニング / グラフ解析 |
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| Outline of Annual Research Achievements |
Optimal transport (OT) has recently gained significant attention in the machine learning community, particularly its ability to capture geometric relationships between data distributions. The computational demands of OT, however, limit their practicality for large-scale problems, a challenge compounded by the complexities and GPU parallelization issues in existing linear programming algorithms. Most existing methods for accelerating OT focus on single distribution problems and do not exploit the common features of the distributions. We propose a translated problem of OT problem, called Basis Optimal Transport (BOT), that can handle multiple distribution problems more efficiently. In BOT, the distributions are projected onto a shared basis space, which avoids kernel computation for each distribution pair. Additionally, we introduceｄ a novel approach for accelerating unbalanced optimal transport (UOT) problems. This method effectively identifies and ignores zero elements in the solution without compromising quality. Traditional techniques falter due to the limitations of conventional projection methods, particularly in handling only the l2-penalized UOT problem. Our new projection method overcomes these limitations, reducing projection errors and adapting to the unique structure of UOT problems.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
当初の目的通り，研究は進んでいる．特に，並列計算のためのサブスペースベースの手法，スクリーニング技術を用いた高速化手法の研究成果がでている．2024年度は対外発表を進めていく．
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| Strategy for Future Research Activity |
応用問題も見越したアルゴリズムの構築も視野にいれることで，研究の広がりを模索していく.
また対外発表を進めていく．
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| Causes of Carryover |
国際会議等への発表に使用していく．
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