Title: Structured Optimal Transport,
Abstract: Optimal Transport has recently gained interest in machine learning for
applications ranging from domain adaptation, sentence similarities to 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 to reflect 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.