Multi-source transfer learning incurs an intrinsic adaptation cost that can exceed one, with phase transitions separating regimes where bias-agnostic estimators match oracle performance from those where they cannot.
Structured Optimal Transport
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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.
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UNVERDICTED 2representative citing papers
Defines Hausdorff-style and Wasserstein-style metrics on C-sets, proving the latter are convex relaxations of the former and computable as linear programs.
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The Statistical Cost of Adaptation in Multi-Source Transfer Learning
Multi-source transfer learning incurs an intrinsic adaptation cost that can exceed one, with phase transitions separating regimes where bias-agnostic estimators match oracle performance from those where they cannot.
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Hausdorff and Wasserstein metrics on graphs and other structured data
Defines Hausdorff-style and Wasserstein-style metrics on C-sets, proving the latter are convex relaxations of the former and computable as linear programs.