# Distributed Differentially Private Computation of Functions with Correlated Noise

arXiv: https://arxiv.org/abs/1904.10059 · HTML: https://mlsanity.com/paper/1904.10059/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2019.

## Built on by (most cited first, 3 of 3)

- [The Privacy Power of Correlated Noise in Decentralized Learning](https://mlsanity.com/paper/2405.01031/) (2024)
- [Federated singular value decomposition for high dimensional data](https://mlsanity.com/paper/2205.12109/) (2022)
- [Dropout-Robust Mechanisms for Differentially Private and Fully Decentralized Mean Estimation](https://mlsanity.com/paper/2506.03746/) (2025)

## Abstract (arXiv)

Many applications of machine learning, such as human health research, involve processing private or sensitive information. Privacy concerns may impose significant hurdles to collaboration in scenarios where there are multiple sites holding data and the goal is to estimate properties jointly across all datasets. Differentially private decentralized algorithms can provide strong privacy guarantees. However, the accuracy of the joint estimates may be poor when the datasets at each site are small. This paper proposes a new framework, Correlation Assisted Private Estimation (CAPE), for designing privacy-preserving decentralized algorithms with better accuracy guarantees in an honest-but-curious model. CAPE can be used in conjunction with the functional mechanism for statistical and machine learning optimization problems. A tighter characterization of the functional mechanism is provided that allows CAPE to achieve the same performance as a centralized algorithm in the decentralized setting using all datasets. Empirical results on regression and neural network problems for both synthetic and real datasets show that differentially private methods can be competitive with non-private algorithms in many scenarios of interest.