Order Constraints in Optimal Transport

Yu Chin Fabian Lim, Laura Wynter, Shiau Hong Lim
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:13313-13333, 2022.

Abstract

Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure. We introduce novel order constraints into the optimal transport formulation to allow for the incorporation of structure. We define an efficient method for obtaining explainable solutions to the new formulation that scales far better than standard approaches. The theoretical properties of the method are provided. We demonstrate experimentally that order constraints improve explainability using the e-SNLI (Stanford Natural Language Inference) dataset that includes human-annotated rationales as well as on several image color transfer examples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-lim22b, title = {Order Constraints in Optimal Transport}, author = {Lim, Yu Chin Fabian and Wynter, Laura and Lim, Shiau Hong}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {13313--13333}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/lim22b/lim22b.pdf}, url = {https://proceedings.mlr.press/v162/lim22b.html}, abstract = {Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure. We introduce novel order constraints into the optimal transport formulation to allow for the incorporation of structure. We define an efficient method for obtaining explainable solutions to the new formulation that scales far better than standard approaches. The theoretical properties of the method are provided. We demonstrate experimentally that order constraints improve explainability using the e-SNLI (Stanford Natural Language Inference) dataset that includes human-annotated rationales as well as on several image color transfer examples.} }
Endnote
%0 Conference Paper %T Order Constraints in Optimal Transport %A Yu Chin Fabian Lim %A Laura Wynter %A Shiau Hong Lim %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-lim22b %I PMLR %P 13313--13333 %U https://proceedings.mlr.press/v162/lim22b.html %V 162 %X Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure. We introduce novel order constraints into the optimal transport formulation to allow for the incorporation of structure. We define an efficient method for obtaining explainable solutions to the new formulation that scales far better than standard approaches. The theoretical properties of the method are provided. We demonstrate experimentally that order constraints improve explainability using the e-SNLI (Stanford Natural Language Inference) dataset that includes human-annotated rationales as well as on several image color transfer examples.
APA
Lim, Y.C.F., Wynter, L. & Lim, S.H.. (2022). Order Constraints in Optimal Transport. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:13313-13333 Available from https://proceedings.mlr.press/v162/lim22b.html.

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