Differentially Private Wasserstein Barycenters

2025/10/03 by Anming Gu, Gu, Anming, Sasidhar Kunapuli +7
Computer Science · Mathematics · #Privacy-Preserving Technologies in Data #Stochastic Gradient Optimization Techniques #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2510.03021

Abstract

The Wasserstein barycenter is defined as the mean of a set of probability measures under the optimal transport metric, and has numerous applications spanning machine learning, statistics, and computer graphics. In practice these input measures are empirical distributions built from sensitive datasets, motivating a differentially private (DP) treatment. We present, to our knowledge, the first algorithms for computing Wasserstein barycenters under differential privacy. Empirically, on synthetic data, MNIST, and large-scale U.S. population datasets, our methods produce high-quality private barycenters with strong accuracy-privacy tradeoffs.

Citations

• Instance-Optimal Private Density Estimation in the Wasserstein Distance
• Algorithmically Effective Differentially Private Synthetic Data
• Private Query Release via the Johnson-Lindenstrauss Transform
• The Johnson-Lindenstrauss Lemma for Clustering and Subspace Approximation: From Coresets to Dimension Reduction
• Improved Approximations for Euclidean k-means and k-median, via Nested Quasi-Independent Sets
• An Improved Local Search Algorithm for k-Median
• Dimensionality Reduction for Wasserstein Barycenter
• Winning the NIST Contest: A scalable and general approach to differentially private synthetic data
• Randomized Dimensionality Reduction for Facility Location and Single-Linkage Clustering
• Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples
• Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applications
• k-Variance: A Clustered Notion of Variance
• Differentially private k-means clustering via exponential mechanism and max cover
• Differentially Private Clustering via Maximum Coverage
• Differentially Private Clustering: Tight Approximation Ratios
• Multimarginal Wasserstein Barycenter for Stain Normalization and\n Augmentation
• LinkedIn's Audience Engagements API: A Privacy Preserving Data Analytics System at Scale
• Gaussian-Smooth Optimal Transport: Metric Structure and Statistical Efficiency
• Convergence of Smoothed Empirical Measures with Applications to Entropy\n Estimation
• Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
• Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity
• Performance of Johnson-Lindenstrauss Transform for k-Means and k-Medians Clustering
• Sample Complexity of Sinkhorn divergences
• Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences
• Differentially Private k-Means with Constant Multiplicative Error
• Differentially Private Generative Adversarial Network
• Stochastic Wasserstein Barycenters
• Collecting Telemetry Data Privately
• Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
• Iterative Bregman Projections for Regularized Transportation Problems
• Learning Probability Measures with respect to Optimal Transport Metrics
• The Johnson-Lindenstrauss Transform Itself Preserves Differential Privacy
• Differentially Private Combinatorial Optimization
• Greedy Facility Location Algorithms Analyzed using Dual Fitting with Factor-Revealing LP
• Approximation algorithms for metric facility location and k -Median problems using the primal-dual schema and Lagrangian relaxation
• Least squares quantization in PCM

Related

• Learning with Differentially Private (Sliced) Wasserstein Gradients
• Wasserstein Differential Privacy
• Algorithmically Effective Differentially Private Synthetic Data
• Stochastic Wasserstein Barycenters
• Private Wasserstein Distance