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Many applications of machine learning, such as human health research, involveprocessing private or sensitive information. Privacy concerns may imposesignificant hurdles to collaboration in scenarios where there are multiplesites holding data and the goal is to estimate properties jointly across alldatasets. Differentially private decentralized algorithms can provide strongprivacy guarantees. However, the accuracy of the joint estimates may be poorwhen the datasets at each site are small. This paper proposes a new framework,Correlation Assisted Private Estimation (CAPE), for designingprivacy-preserving decentralized algorithms with better accuracy guarantees inan honest-but-curious model. CAPE can be used in conjunction with thefunctional mechanism for statistical and machine learning optimizationproblems. A tighter characterization of the functional mechanism is providedthat allows CAPE to achieve the same performance as a centralized algorithm inthe decentralized setting using all datasets. Empirical results on regressionand neural network problems for both synthetic and real datasets show thatdifferentially private methods can be competitive with non-private algorithmsin many scenarios of interest.

Distributed Differentially Private Computation of Functions with Correlated Noise