Optimal Transportation and Applications
timetable:
Thu 5 Dec, 16:25 - 16:55, Aula Dini
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Sliced-Wasserstein distance for generative modeling and unbalanced optimal transport
speaker: Kimia Nadjahi (CNRS, ENS Paris)abstract: We study the Sliced-Wasserstein distance (SW) from a theoretical perspective, driven by modern challenges in machine learning and generative modeling. We show that SW retains some key topological properties of the Wasserstein distance, while offering greater robustness in high-dimensional settings. Then, we introduce a novel framework for efficiently comparing arbitrary positive measures by combining the concepts of "slicing" and "unbalancing" optimal transport. We formulate two variants of "sliced unbalanced optimal transport" and derive the associated dual problems, which enables the development of a Frank-Wolfe algorithm for efficient computation. The talk concludes with a discussion of open questions surrounding SW.
timetable:
Thu 5 Dec, 16:25 - 16:55, Aula Dini
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