Structured Optimal Transport

David Alvarez-Melis, Tommi Jaakkola, Stefanie Jegelka
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1771-1780, 2018.

Abstract

Optimal 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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-alvarez-melis18a, title = {Structured Optimal Transport}, author = {Alvarez-Melis, David and Jaakkola, Tommi and Jegelka, Stefanie}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1771--1780}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/alvarez-melis18a/alvarez-melis18a.pdf}, url = {https://proceedings.mlr.press/v84/alvarez-melis18a.html}, abstract = {Optimal 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 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.} }
Endnote
%0 Conference Paper %T Structured Optimal Transport %A David Alvarez-Melis %A Tommi Jaakkola %A Stefanie Jegelka %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-alvarez-melis18a %I PMLR %P 1771--1780 %U https://proceedings.mlr.press/v84/alvarez-melis18a.html %V 84 %X Optimal 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 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.
APA
Alvarez-Melis, D., Jaakkola, T. & Jegelka, S.. (2018). Structured Optimal Transport. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1771-1780 Available from https://proceedings.mlr.press/v84/alvarez-melis18a.html.

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