| 配分額 *注記 |
4,290千円 (直接経費: 3,300千円、間接経費: 990千円)
2024年度: 1,560千円 (直接経費: 1,200千円、間接経費: 360千円)
2023年度: 1,690千円 (直接経費: 1,300千円、間接経費: 390千円)
2022年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
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| 研究実績の概要 |
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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