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On Transportation of Mini-batches: A Hierarchical Approach
Khai Nguyen · Dang Nguyen · Quoc Nguyen · Tung Pham · Hung Bui · Dinh Phung · Trung Le · Nhat Ho

Wed Jul 20 07:45 AM -- 07:50 AM (PDT) @ Ballroom 3 & 4

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.

Author Information

Khai Nguyen (University of Texas at Austin)
Dang Nguyen (VinAI)
Dang Nguyen

AI Resident

Quoc Nguyen (VinAI)
Tung Pham (VinAI Research)
Hung Bui (VinAI Research)
Dinh Phung (Monash University, Australia)
Trung Le (Monash University)
Nhat Ho (University of Texas at Austin)

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