no code implementations • 6 Feb 2024 • Yikun Bai, Rocio Diaz Martin, Hengrong Du, Ashkan Shahbazi, Soheil Kolouri
The partial Gromov-Wasserstein (PGW) problem facilitates the comparison of measures with unequal masses residing in potentially distinct metric spaces, thereby enabling unbalanced and partial matching across these spaces.
no code implementations • 4 Feb 2024 • Huy Tran, Yikun Bai, Abihith Kothapalli, Ashkan Shahbazi, Xinran Liu, Rocio Diaz Martin, Soheil Kolouri
Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning.
no code implementations • 9 Oct 2023 • Rocio Diaz Martin, Ivan Medri, Yikun Bai, Xinran Liu, Kangbai Yan, Gustavo K. Rohde, Soheil Kolouri
The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning.
no code implementations • 27 Sep 2023 • Yikun Bai, Huy Tran, Steven B. Damelin, Soheil Kolouri
In this paper, we approach the point-cloud registration problem through the lens of optimal transport theory and first propose a comprehensive set of non-rigid registration methods based on the optimal partial transportation problem.
no code implementations • 25 Jul 2023 • Xinran Liu, Yikun Bai, Huy Tran, Zhanqi Zhu, Matthew Thorpe, Soheil Kolouri
In this paper, we introduce partial transport $\mathrm{L}^{p}$ distances as a new family of metrics for comparing generic signals, benefiting from the robustness of partial transport distances.
1 code implementation • 7 Feb 2023 • Yikun Bai, Ivan Medri, Rocio Diaz Martin, Rana Muhammad Shahroz Khan, Soheil Kolouri
To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed.
2 code implementations • CVPR 2023 • Yikun Bai, Berhnard Schmitzer, Mathew Thorpe, Soheil Kolouri
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision.
1 code implementation • 24 Aug 2022 • Xinran Liu, Yikun Bai, Yuzhe Lu, Andrea Soltoggio, Soheil Kolouri
Lastly, we leverage the 2-Wasserstein embedding framework to embed tasks into a vector space in which the Euclidean distance between the embedded points approximates the proposed 2-Wasserstein distance between tasks.
no code implementations • 2 Nov 2021 • Daria Reshetova, Yikun Bai, Xiugang Wu, Ayfer Ozgur
We show that the optimal generator can be learned to accuracy $\epsilon$ with $O(1/\epsilon^2)$ samples from the target distribution.
no code implementations • 24 Aug 2020 • Yikun Bai, Xiugang Wu, Ayfer Ozgur
Following Marton's approach, we show that the new transportation cost inequality can be used to recover old and new concentration of measure results.