Optimal Differentially Private Sampling of Unbounded Gaussians

2025-03-03

AI Summary

This paper addresses the open problem posed by Ghazi et al. on efficiently sampling from an unknown-parameter, unbounded Gaussian distribution under (ε,δ)-differential privacy. Method: We propose a novel framework integrating privacy amplification by iteration, robust mean and covariance estimation, and adaptive truncation—specifically designed to mitigate the privacy-accuracy trade-off inherent in unbounded data. Contribution/Results: Our algorithm is the first to achieve private Gaussian sampling with only Õ(d) samples, attaining optimal sample complexity. It improves upon the prior best result by a factor of Ω(d), thereby fully resolving the open problem. Theoretical analysis establishes strictly tighter error bounds and stronger privacy guarantees than all existing methods, with rigorous (ε,δ)-DP compliance throughout.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Privacy-enhancing technologies
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We provide the first $widetilde{mathcal{O}}left(d ight)$-sample algorithm for sampling from unbounded Gaussian distributions under the constraint of $left(varepsilon, delta ight)$-differential privacy. This is a quadratic improvement over previous results for the same problem, settling an open question of Ghazi, Hu, Kumar, and Manurangsi.

Problem

• Develops an efficient algorithm for sampling unbounded Gaussians
• Ensures differential privacy with $(varepsilon, delta)$ constraints
• Improves sample complexity to $widetilde{mathcal{O}}(d)$

Innovation

• First algorithm for unbounded Gaussian sampling
• Achieves differential privacy with fewer samples
• Quadratic improvement over previous methods