# Learning with Differentially Private (Sliced) Wasserstein Gradients

arXiv: https://arxiv.org/abs/2502.01701 · HTML: https://mlsanity.com/paper/2502.01701/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 106 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 30 of 56)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Opacus: User-Friendly Differential Privacy Library in PyTorch](https://mlsanity.com/paper/2109.12298/) (2021)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1903.04064/) (2019)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [DP-MERF: Differentially Private Mean Embeddings with Random Features for Practical Privacy-Preserving Data Generation](https://mlsanity.com/paper/2002.11603/) (2020)
- [Differentially Private Fair Learning](https://mlsanity.com/paper/1812.02696/) (2018)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [Sliced Wasserstein Generative Models](https://mlsanity.com/paper/1904.05408/) (2019)
- [Neither Private Nor Fair: Impact of Data Imbalance on Utility and Fairness in Differential Privacy](https://mlsanity.com/paper/2009.06389/) (2020)
- [Private Hypothesis Selection](https://mlsanity.com/paper/1905.13229/) (2019)
- [Differentially Private Assouad, Fano, and Le Cam](https://mlsanity.com/paper/2004.06830/) (2020)
- [Scaling up Differentially Private Deep Learning with Fast Per-Example Gradient Clipping](https://mlsanity.com/paper/2009.03106/) (2020)
- [Improved Rates for Differentially Private Stochastic Convex Optimization with Heavy-Tailed Data](https://mlsanity.com/paper/2106.01336/) (2021)
- [Differential Privacy and Fairness in Decisions and Learning Tasks: A Survey](https://mlsanity.com/paper/2202.08187/) (2022)
- [Covariance-Aware Private Mean Estimation Without Private Covariance Estimation](https://mlsanity.com/paper/2106.13329/) (2021)

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

- [Differentially Private Sampling from Distributions via Wasserstein Projection](https://mlsanity.com/paper/2605.10015/) (2026)
- [Convergence of empirical subgradients for optimal transport-based objectives](https://mlsanity.com/paper/2605.28134/) (2026)

## 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.