Learning with Differentially Private (Sliced) Wasserstein Gradients
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Abstract (arXiv)
In this work, we introduce a novel framework for privately optimizing objectives that rely on Wasserstein distances between data-dependent empirical measures. Our main theoretical contribution is, based on an explicit formulation of the Wasserstein gradient in a fully discrete setting, a control on the sensitivity of this gradient to individual data points, allowing strong privacy guarantees at minimal utility cost. Building on these insights, we develop a deep learning approach that incorporates gradient and activations clipping, originally designed for DP training of problems with a finite-sum structure. We further demonstrate that privacy accounting methods extend to Wasserstein-based objectives, facilitating large-scale private training. Empirical results confirm that our framework effectively balances accuracy and privacy, offering a theoretically sound solution for privacy-preserving machine learning tasks relying on optimal transport distances such as Wasserstein distance or sliced-Wasserstein distance.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 56 of its 106 references that are in the map. First posted on arXiv 3 Feb 2025.
Builds on
56 of 106 references.
References · 56
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38 more
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- 2019Wasserstein Fair Classificationcited by 131
- 2018Generative Modeling using the Sliced Wasserstein Distancecited by 108
- 2017Finite Sample Differentially Private Confidence Intervalscited by 103
- 2018Privately Learning High-Dimensional Distributionscited by 103
- 2020Fair Regression with Wasserstein Barycenterscited by 99
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- 2020CoinPress: Practical Private Mean and Covariance Estimationcited by 74
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- 2019Sliced Wasserstein Generative Modelscited by 61
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- 2022Differential Privacy has Bounded Impact on Fairness in Classificationcited by 18
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- 2023Properties of Discrete Sliced Wasserstein Lossescited by 12
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- 2024Differentially Private Post-Processing for Fair Regressioncited by 5
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Citing papers per year: 2026: 2.
2 papers.