On Transportation of Mini-batches: A Hierarchical Approach

Khai Nguyen, Dang Nguyen, Quoc Dinh Nguyen, Tung Pham, Hung Bui, Dinh Phung, Trung Le, Nhat Ho
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:16622-16655, 2022.

Abstract

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with a very high number of supports. The m-OT solves several smaller optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batch scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out experiments on various applications including deep generative models, deep domain adaptation, approximate Bayesian computation, color transfer, and gradient flow to show that the BoMb-OT can be widely applied and performs well in various applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-nguyen22d, title = {On Transportation of Mini-batches: A Hierarchical Approach}, author = {Nguyen, Khai and Nguyen, Dang and Nguyen, Quoc Dinh and Pham, Tung and Bui, Hung and Phung, Dinh and Le, Trung and Ho, Nhat}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {16622--16655}, 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/nguyen22d/nguyen22d.pdf}, url = {https://proceedings.mlr.press/v162/nguyen22d.html}, abstract = {Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with a very high number of supports. The m-OT solves several smaller optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batch scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out experiments on various applications including deep generative models, deep domain adaptation, approximate Bayesian computation, color transfer, and gradient flow to show that the BoMb-OT can be widely applied and performs well in various applications.} }
Endnote
%0 Conference Paper %T On Transportation of Mini-batches: A Hierarchical Approach %A Khai Nguyen %A Dang Nguyen %A Quoc Dinh Nguyen %A Tung Pham %A Hung Bui %A Dinh Phung %A Trung Le %A Nhat Ho %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-nguyen22d %I PMLR %P 16622--16655 %U https://proceedings.mlr.press/v162/nguyen22d.html %V 162 %X Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with a very high number of supports. The m-OT solves several smaller optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batch scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out experiments on various applications including deep generative models, deep domain adaptation, approximate Bayesian computation, color transfer, and gradient flow to show that the BoMb-OT can be widely applied and performs well in various applications.
APA
Nguyen, K., Nguyen, D., Nguyen, Q.D., Pham, T., Bui, H., Phung, D., Le, T. & Ho, N.. (2022). On Transportation of Mini-batches: A Hierarchical Approach. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:16622-16655 Available from https://proceedings.mlr.press/v162/nguyen22d.html.

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