# Wasserstein Distances Made Explainable: Insights Into Dataset Shifts and Transport Phenomena

arXiv: https://arxiv.org/abs/2505.06123 · HTML: https://mlsanity.com/paper/2505.06123/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 83 references that are in the map.
- First posted on arXiv 9 May 2025.

## Builds on (most cited first, 30 of 44)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Explainable Machine Learning for Scientific Insights and Discoveries](https://mlsanity.com/paper/1905.08883/) (2019)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [CLIP-Dissect: Automatic Description of Neuron Representations in Deep Vision Networks](https://mlsanity.com/paper/2204.10965/) (2022)
- [Self supervised contrastive learning for digital histopathology](https://mlsanity.com/paper/2011.13971/) (2020)
- [From Attribution Maps to Human-Understandable Explanations through Concept Relevance Propagation](https://mlsanity.com/paper/2206.03208/) (2022)
- [Higher-Order Explanations of Graph Neural Networks via Relevant Walks](https://mlsanity.com/paper/2006.03589/) (2020)
- [XAI for Transformers: Better Explanations through Conservative Propagation](https://mlsanity.com/paper/2202.07304/) (2022)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Benchmarking Distribution Shift in Tabular Data with TableShift](https://mlsanity.com/paper/2312.07577/) (2023)
- [Outlier-Robust Optimal Transport](https://mlsanity.com/paper/2012.07363/) (2020)
- [CO-Optimal Transport](https://mlsanity.com/paper/2002.03731/) (2020)
- [Why did the distribution change?](https://mlsanity.com/paper/2102.13384/) (2021)
- [Distilling foundation models for robust and efficient models in digital pathology](https://mlsanity.com/paper/2501.16239/) (2025)
- [From Clustering to Cluster Explanations via Neural Networks](https://mlsanity.com/paper/1906.07633/) (2019)
- [Structured Optimal Transport](https://mlsanity.com/paper/1712.06199/) (2017)
- [The Rashomon Importance Distribution: Getting RID of Unstable, Single Model-based Variable Importance](https://mlsanity.com/paper/2309.13775/) (2023)

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

- [Explanation of Dynamic Physical Field Predictions using WassersteinGrad: Application to Autoregressive Weather Forecasting](https://mlsanity.com/paper/2604.22580/) (2026)
- [Reliable Modeling of Distribution Shifts via Displacement-Reshaped Optimal Transport](https://mlsanity.com/paper/2605.04965/) (2026)

## Abstract (arXiv)

Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing the corresponding transport plan (or coupling) may not be sufficient for understanding what factors contribute to a high or low Wasserstein distance. In this work, we propose a novel solution based on Explainable AI that allows us to efficiently and accurately attribute Wasserstein distances to various data components, including data subgroups, input features, or interpretable subspaces. Our method achieves high accuracy across diverse datasets and Wasserstein distance specifications, and its practical utility is demonstrated in three use cases.