Improving Mini-batch Optimal Transport via Partial Transportation

Khai Nguyen, Dang Nguyen, Tung Pham, Nhat Ho

Keywords: Deep Domain Adaptation, Deep Generative Models, Color Transfer, Optimal Transport

Abstract: Mini-batch optimal transport (m-OT) has been widely used recently to deal with the memory issue of OT in large-scale applications. Despite their practicality, m-OT suffers from misspecified mappings, namely, mappings that are optimal on the mini-batch level but are partially wrong in the comparison with the optimal transportation plan between the original measures. To address the misspecified mappings issue, we propose a novel mini-batch method by using partial optimal transport (POT) between mini-batch empirical measures, which we refer to as mini-batch partial optimal transport (m-POT). Leveraging the insight from the partial transportation, we explain the source of misspecified mappings from the m-OT and motivate why limiting the amount of transported masses among mini-batches via POT can alleviate the incorrect mappings. Finally, we carry out extensive experiments on various applications to compare m-POT with m-OT and recently proposed mini-batch method, mini-batch unbalanced optimal transport (m-UOT). We observe that m-POT is better than m-OT in deep domain adaptation applications while having comparable performance with m-UOT. On other applications, such as deep generative model and color transfer, m-POT yields more favorable performance than m-OT while m-UOT is non-trivial to apply.

One-sentence Summary: The paper suggests replacing Optimal Transport with partial Optimal Transport to alleviate misspecified mappings in applications that uses mini-batches such as deep domain adaptation, deep generative models, and color transfer.