Alvarez Melis, DavidJaakkola, Tommi S.Jegelka, Stefanie2025-05-132018-04-09D. Alvarez-Melis, T. Jaakkola, and S. Jegelka. "Structured Optimal Transport". In: Proc. Twenty-First International Conference on Artificial Intelligence and Statistics. AISTATS. Ed. by A. Storkey and F. Perez-Cruz. Vol. 84. Proceedings of Machine Learning Research. PMLR, 2018.https://dash.harvard.edu/handle/1/42717542Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation to sentence similarities or deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground metric" is limited. In this work, we develop a nonlinear generalization of (discrete) optimal transport that is able toreflect much additional structure. We demonstrate how to leverage the geometry of this new model for fast algorithms, and explore connections and properties. Illustrative experiments highlight the benefit of the induced structured couplings for tasks in domain adaptation and natural language processing.EnglishConference Proceedings