On Scalable and Efficient Computation of Large Scale Optimal Transport

Yujia Xie, Minshuo Chen, Haoming Jiang, Tuo Zhao, Hongyuan Zha
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6882-6892, 2019.

Abstract

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-xie19a, title = {On Scalable and Efficient Computation of Large Scale Optimal Transport}, author = {Xie, Yujia and Chen, Minshuo and Jiang, Haoming and Zhao, Tuo and Zha, Hongyuan}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {6882--6892}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/xie19a/xie19a.pdf}, url = {https://proceedings.mlr.press/v97/xie19a.html}, abstract = {Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.} }
Endnote
%0 Conference Paper %T On Scalable and Efficient Computation of Large Scale Optimal Transport %A Yujia Xie %A Minshuo Chen %A Haoming Jiang %A Tuo Zhao %A Hongyuan Zha %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-xie19a %I PMLR %P 6882--6892 %U https://proceedings.mlr.press/v97/xie19a.html %V 97 %X Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework called SPOT (Scalable Push-forward of Optimal Transport). Specifically, we approximate the optimal transport plan by a pushforward of a reference distribution, and cast the optimal transport problem into a minimax problem. We then can solve OT problems efficiently using primal dual stochastic gradient-type algorithms. We also show that we can recover the density of the optimal transport plan using neural ordinary differential equations. Numerical experiments on both synthetic and real datasets illustrate that SPOT is robust and has favorable convergence behavior. SPOT also allows us to efficiently sample from the optimal transport plan, which benefits downstream applications such as domain adaptation.
APA
Xie, Y., Chen, M., Jiang, H., Zhao, T. & Zha, H.. (2019). On Scalable and Efficient Computation of Large Scale Optimal Transport. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6882-6892 Available from https://proceedings.mlr.press/v97/xie19a.html.

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