# Inference via robust optimal transportation: theory and methods

arXiv: https://arxiv.org/abs/2301.06297 · HTML: https://mlsanity.com/paper/2301.06297/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 54 references that are in the map.
- First posted on arXiv 16 Jan 2023.

## Builds on (most cited first, 13 of 13)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [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)
- [Neural Unsupervised Domain Adaptation in NLP---A Survey](https://mlsanity.com/paper/2006.00632/) (2020)
- [Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation](https://mlsanity.com/paper/2010.05862/) (2020)
- [Sliced Wasserstein Kernel for Persistence Diagrams](https://mlsanity.com/paper/1706.03358/) (2017)
- [Outlier-Robust Optimal Transport](https://mlsanity.com/paper/2012.07363/) (2020)
- [Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces](https://mlsanity.com/paper/1804.10556/) (2018)
- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
- [Nonparametric Multiple-Output Center-Outward Quantile Regression](https://mlsanity.com/paper/2204.11756/) (2022)
- [Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem](https://mlsanity.com/paper/1709.10219/) (2017)

## Built on by (most cited first, 2 of 2)

- [On Robust Cross Domain Alignment](https://mlsanity.com/paper/2412.15861/) (2024)
- [Robust OT-Guided Generative Residual Domain Adaptation for Bike-Sharing Demand Prediction under Temporal Domain Shift](https://mlsanity.com/paper/2605.23115/) (2026)

## Abstract (arXiv)

Optimal transportation theory and the related p-Wasserstein distance (Wp, p≥ 1) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it is sensitive to outliers and it may not be even defined when the underlying model has infinite moments. To cope with these problems, first we consider a robust version of the primal transportation problem and show that it defines the robust Wasserstein distance, W(λ), depending on a tuning parameter λ > 0. Second, we illustrate the link between W1 and W(λ) and study its key measure theoretic aspects. Third, we derive some concentration inequalities for W(λ). Fourth, we use W(λ) to define minimum distance estimators, we provide their statistical guarantees and we illustrate how to apply the derived concentration inequalities for a data driven selection of λ. Fifth, we provide the dual form of the robust optimal transportation problem and we apply it to machine learning problems (generative adversarial networks and domain adaptation). Numerical exercises provide evidence of the benefits yielded by our novel methods.