# InfoOT: Information Maximizing Optimal Transport

arXiv: https://arxiv.org/abs/2210.03164 · HTML: https://mlsanity.com/paper/2210.03164/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 73 references that are in the map.
- First posted on arXiv 6 Oct 2022.

## Builds on (most cited first, 30 of 32)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Deep Domain Confusion: Maximizing for Domain Invariance](https://mlsanity.com/paper/1412.3474/) (2014)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Gromov-Wasserstein Alignment of Word Embedding Spaces](https://mlsanity.com/paper/1809.00013/) (2018)
- [Scatter Component Analysis: A Unified Framework for Domain Adaptation and Domain Generalization](https://mlsanity.com/paper/1510.04373/) (2015)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Visual Domain Adaptation with Manifold Embedded Distribution Alignment](https://mlsanity.com/paper/1807.07258/) (2018)
- [Large-Scale Wasserstein Gradient Flows](https://mlsanity.com/paper/2106.00736/) (2021)
- [Training individually fair ML models with Sensitive Subspace Robustness](https://mlsanity.com/paper/1907.00020/) (2019)
- [Wasserstein Dependency Measure for Representation Learning](https://mlsanity.com/paper/1903.11780/) (2019)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [Regularized Discrete Optimal Transport](https://mlsanity.com/paper/1307.5551/) (2013)
- [Outlier-Robust Optimal Transport](https://mlsanity.com/paper/2012.07363/) (2020)
- [Robust Contrastive Learning against Noisy Views](https://mlsanity.com/paper/2201.04309/) (2022)
- [From optimal transport to generative modeling: the VEGAN cookbook](https://mlsanity.com/paper/1705.07642/) (2017)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Towards Optimal Transport with Global Invariances](https://mlsanity.com/paper/1806.09277/) (2018)
- [Structured Optimal Transport](https://mlsanity.com/paper/1712.06199/) (2017)
- [Measuring Generalization with Optimal Transport](https://mlsanity.com/paper/2106.03314/) (2021)
- [When Optimal Transport Meets Information Geometry](https://mlsanity.com/paper/2206.14791/) (2022)

## Built on by (most cited first, 9 of 9)

- [CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels](https://mlsanity.com/paper/2312.06221/) (2023)
- [Revisiting Counterfactual Regression through the Lens of Gromov-Wasserstein Information Bottleneck](https://mlsanity.com/paper/2405.15505/) (2024)
- [Optimal Transport for Domain Adaptation through Gaussian Mixture Models](https://mlsanity.com/paper/2403.13847/) (2024)
- [OT-Net: A Reusable Neural Optimal Transport Solver](https://mlsanity.com/paper/2306.08233/) (2023)
- [DeepEMD: A Transformer-based Fast Estimation of the Earth Mover's Distance](https://mlsanity.com/paper/2311.09998/) (2023)
- [Learning to Match Unpaired Data with Minimum Entropy Coupling](https://mlsanity.com/paper/2503.08501/) (2025)
- [Optimal Transport with Adaptive Regularisation](https://mlsanity.com/paper/2310.02925/) (2023)
- [Geometry-Aware Normalizing Wasserstein Flows for Optimal Causal Inference](https://mlsanity.com/paper/2311.18826/) (2023)
- [A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution](https://mlsanity.com/paper/2606.02515/) (2026)

## Abstract (arXiv)

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and cannot integrate new data points. To address these drawbacks, we propose InfoOT, an information-theoretic extension of optimal transport that maximizes the mutual information between domains while minimizing geometric distances. The resulting objective can still be formulated as a (generalized) optimal transport problem, and can be efficiently solved by projected gradient descent. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples. Empirically, InfoOT improves the quality of alignments across benchmarks in domain adaptation, cross-domain retrieval, and single-cell alignment.