# Correlated Privacy Mechanisms for Differentially Private Distributed Mean Estimation arXiv: https://arxiv.org/abs/2407.03289 · HTML: https://mlsanity.com/paper/2407.03289/ ## Key facts - Cited by 4 papers in the map (data through 14 Oct 2026). - Builds on 38 of its 58 references that are in the map. - First posted on arXiv 3 Jul 2024. ## Builds on (most cited first, 30 of 38) - [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016) - [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017) - [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019) - [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018) - [Practical and Private (Deep) Learning without Sampling or Shuffling](https://mlsanity.com/paper/2103.00039/) (2021) - [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018) - [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018) - [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016) - [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018) - [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021) - [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018) - [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016) - [Breaking the Communication-Privacy-Accuracy Trilemma](https://mlsanity.com/paper/2007.11707/) (2020) - [The Skellam Mechanism for Differentially Private Federated Learning](https://mlsanity.com/paper/2110.04995/) (2021) - [Eluding Secure Aggregation in Federated Learning via Model Inconsistency](https://mlsanity.com/paper/2111.07380/) (2021) - [LightSecAgg: a Lightweight and Versatile Design for Secure Aggregation in Federated Learning](https://mlsanity.com/paper/2109.14236/) (2021) - [(Amplified) Banded Matrix Factorization: A unified approach to private training](https://mlsanity.com/paper/2306.08153/) (2023) - [Encode, Shuffle, Analyze Privacy Revisited: Formalizations and Empirical Evaluation](https://mlsanity.com/paper/2001.03618/) (2020) - [The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning](https://mlsanity.com/paper/2203.03761/) (2022) - [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021) - [Prio: Private, Robust, and Scalable Computation of Aggregate Statistics](https://mlsanity.com/paper/1703.06255/) (2017) - [Optimal Algorithms for Mean Estimation under Local Differential Privacy](https://mlsanity.com/paper/2205.02466/) (2022) - [rTop-k: A Statistical Estimation Approach to Distributed SGD](https://mlsanity.com/paper/2005.10761/) (2020) - [Lossless Compression of Efficient Private Local Randomizers](https://mlsanity.com/paper/2102.12099/) (2021) - [Efficient Differentially Private Secure Aggregation for Federated Learning via Hardness of Learning with Errors](https://mlsanity.com/paper/2112.06872/) (2021) - [Correlated Noise Provably Beats Independent Noise for Differentially Private Learning](https://mlsanity.com/paper/2310.06771/) (2023) - [Optimal Compression of Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2111.00092/) (2021) - [Privacy Amplification via Compression: Achieving the Optimal Privacy-Accuracy-Communication Trade-off in Distributed Mean Estimation](https://mlsanity.com/paper/2304.01541/) (2023) - [Information Theoretic Secure Aggregation with User Dropouts](https://mlsanity.com/paper/2101.07750/) (2021) - [Gradient Descent with Linearly Correlated Noise: Theory and Applications to Differential Privacy](https://mlsanity.com/paper/2302.01463/) (2023) ## Built on by (most cited first, 4 of 4) - [Mitigating Privacy-Utility Trade-off in Decentralized Federated Learning via f-Differential Privacy](https://mlsanity.com/paper/2510.19934/) (2025) - [CorBin-FL: A Differentially Private Federated Learning Mechanism using Common Randomness](https://mlsanity.com/paper/2409.13133/) (2024) - [Dropout-Robust Mechanisms for Differentially Private and Fully Decentralized Mean Estimation](https://mlsanity.com/paper/2506.03746/) (2025) - [Local Differential Privacy with Correlated Noise Achieves Central-DP Optimal Cost](https://mlsanity.com/paper/2605.30476/) (2026) ## Abstract (arXiv) Differentially private distributed mean estimation (DP-DME) is a fundamental building block in privacy-preserving federated learning, where a central server estimates the mean of d-dimensional vectors held by n users while ensuring (ε,δ)-DP. Local differential privacy (LDP) and distributed DP with secure aggregation (SA) are the most common notions of DP used in DP-DME settings with an untrusted server. LDP provides strong resilience to dropouts, colluding users, and adversarial attacks, but suffers from poor utility. In contrast, SA-based DP-DME achieves an O(n) utility gain over LDP in DME, but requires increased communication and computation overheads and complex multi-round protocols to handle dropouts and attacks. In this work, we present a generalized framework for DP-DME, that captures LDP and SA-based mechanisms as extreme cases. Our framework provides a foundation for developing and analyzing a variety of DP-DME protocols that leverage correlated privacy mechanisms across users. To this end, we propose CorDP-DME, a novel DP-DME mechanism based on the correlated Gaussian mechanism, that spans the gap between DME with LDP and distributed DP. We prove that CorDP-DME offers a favorable balance between utility and resilience to dropout and collusion. We provide an information-theoretic analysis of CorDP-DME, and derive theoretical guarantees for utility under any given privacy parameters and dropout/colluding user thresholds. Our results demonstrate that (anti) correlated Gaussian DP mechanisms can significantly improve utility in mean estimation tasks compared to LDP -- even in adversarial settings -- while maintaining better resilience to dropouts and attacks compared to distributed DP.