| Project/Area Number |
22K12175
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 61030:Intelligent informatics-related
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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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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2024: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2023: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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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 / 緩和最適輸送問題 / 非構造データ / メッセージ・パッシング / グラフ分類 / 機械学習 / 最適化 / 最適輸送 |
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| Outline of Research at the Start |
最適輸送問題は，測度論と最適化理論の両輪を基礎に置き，始点から終点への質量保存の制約の下での二つの確率測度間の最小輸送距離を求める問題として定義される．特筆すべき点は，KL情報量等とは異なり確率測度の空間的な位置も考慮可能であり，ベクトル間距離と確率測度間距離の双方を考慮した最適輸送距離が定義可能になる点にある．これに加えて，数学的定義式が微分可能であることから，近年，この最適輸送距離は多くの機械学習問題で用いられている．そこで本研究では，最適輸送問題の更なる発展を目指し，最適輸送問題求解のための最適化手法と，最適輸送問題の半教師有り学習への応用および非構造データ学習への応用について研究する．
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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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