# Improving Mini-batch Optimal Transport via Partial Transportation

arXiv: https://arxiv.org/abs/2108.09645 · HTML: https://mlsanity.com/paper/2108.09645/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 68 references that are in the map.
- First posted on arXiv 22 Aug 2021.

## Builds on (most cited first, 30 of 38)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Partial Adversarial Domain Adaptation](https://mlsanity.com/paper/1808.04205/) (2018)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Learning to Transfer Examples for Partial Domain Adaptation](https://mlsanity.com/paper/1903.12230/) (2019)
- [Learning with minibatch Wasserstein : asymptotic and gradient properties](https://mlsanity.com/paper/1910.04091/) (2019)
- [Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation](https://mlsanity.com/paper/2010.05862/) (2020)
- [Distributional Sliced-Wasserstein and Applications to Generative Modeling](https://mlsanity.com/paper/2002.07367/) (2020)
- [Sliced Wasserstein Kernels for Probability Distributions](https://mlsanity.com/paper/1511.03198/) (2015)
- [Adversarial-Learned Loss for Domain Adaptation](https://mlsanity.com/paper/2001.01046/) (2020)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithm](https://mlsanity.com/paper/2002.03293/) (2020)
- [A Balanced and Uncertainty-aware Approach for Partial Domain Adaptation](https://mlsanity.com/paper/2003.02541/) (2020)
- [Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization](https://mlsanity.com/paper/2102.01752/) (2021)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)

## Built on by (most cited first, 30 of 41)

- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Unified Optimal Transport Framework for Universal Domain Adaptation](https://mlsanity.com/paper/2210.17067/) (2022)
- [Categorical Flow Matching on Statistical Manifolds](https://mlsanity.com/paper/2405.16441/) (2024)
- [Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution](https://mlsanity.com/paper/2204.01188/) (2022)
- [Hierarchical Sliced Wasserstein Distance](https://mlsanity.com/paper/2209.13570/) (2022)
- [Kantorovich Strikes Back! Wasserstein GANs are not Optimal Transport?](https://mlsanity.com/paper/2206.07767/) (2022)
- [Amortized Projection Optimization for Sliced Wasserstein Generative Models](https://mlsanity.com/paper/2203.13417/) (2022)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Accelerating Sinkhorn Algorithm with Sparse Newton Iterations](https://mlsanity.com/paper/2401.12253/) (2024)
- [Revisiting Deep Audio-Text Retrieval Through the Lens of Transportation](https://mlsanity.com/paper/2405.10084/) (2024)
- [Approximating 1-Wasserstein Distance with Trees](https://mlsanity.com/paper/2206.12116/) (2022)
- [InfoOT: Information Maximizing Optimal Transport](https://mlsanity.com/paper/2210.03164/) (2022)
- [Hierarchical Refinement: Optimal Transport to Infinity and Beyond](https://mlsanity.com/paper/2503.03025/) (2025)
- [Linear Optimal Partial Transport Embedding](https://mlsanity.com/paper/2302.03232/) (2023)
- [On Partial Optimal Transport: Revising the Infeasibility of Sinkhorn and Efficient Gradient Methods](https://mlsanity.com/paper/2312.13970/) (2023)
- [Prototypical Partial Optimal Transport for Universal Domain Adaptation](https://mlsanity.com/paper/2408.01089/) (2024)
- [AlignFlow: Improving Flow-based Generative Models with Semi-Discrete Optimal Transport](https://mlsanity.com/paper/2510.15038/) (2025)
- [Group-blind optimal transport to group parity and its constrained variants](https://mlsanity.com/paper/2310.11407/) (2023)
- [Prompt-OT: An Optimal Transport Regularization Paradigm for Knowledge Preservation in Vision-Language Model Adaptation](https://mlsanity.com/paper/2503.08906/) (2025)
- [Interpolation for Robust Learning: Data Augmentation on Wasserstein Geodesics](https://mlsanity.com/paper/2302.02092/) (2023)
- [A Sinkhorn-type Algorithm for Constrained Optimal Transport](https://mlsanity.com/paper/2403.05054/) (2024)
- [SemRoDe: Macro Adversarial Training to Learn Representations That are Robust to Word-Level Attacks](https://mlsanity.com/paper/2403.18423/) (2024)
- [ContinualFlow: Learning and Unlearning with Neural Flow Matching](https://mlsanity.com/paper/2506.18747/) (2025)
- [COT-FM: Cluster-wise Optimal Transport Flow Matching](https://mlsanity.com/paper/2603.13395/) (2026)
- [Graph Matching Optimization Network for Point Cloud Registration](https://mlsanity.com/paper/2302.05844/) (2023)
- [A Unified Framework for Unsupervised Domain Adaptation based on Instance Weighting](https://mlsanity.com/paper/2312.05024/) (2023)
- [Partial Domain Adaptation via Importance Sampling-based Shift Correction](https://mlsanity.com/paper/2507.20191/) (2025)
- [Amortized Optimal Transport from Sliced Potentials](https://mlsanity.com/paper/2604.15114/) (2026)
- [Geometry-Aware Image Flow Matching](https://mlsanity.com/paper/2605.25294/) (2026)

## Abstract (arXiv)

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. Motivated by 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 such as deep domain adaptation, partial domain adaptation, deep generative model, color transfer, and gradient flow to demonstrate the favorable performance of m-POT compared to current mini-batch methods.