Many applications of machine learning, for example in health care, would benefit from methods that can guarantee privacy of data subjects. Differential privacy (DP) has become established as a standard for protecting learning results, but the proposed algorithms require a single trusted party to have access to the entire data, which is a clear weakness. We consider DP Bayesian learning in a distributed setting, where each party only holds a single sample or a few samples of the data. We propose a novel method for DP learning in this distributed setting, based on a secure multi-party sum function for aggregating summaries from the data holders. Each data holder adds their share of Gaussian noise to make the total computation differentially private using the Gaussian mechanism. We prove that the system can be made secure against a desired number of colluding data owners and robust against faulting data owners. The method builds on an asymptotically optimal and practically efficient DP Bayesian inference with rapidly diminishing extra cost.
Finally, @cite_17 presents several proofs related to the SMC setting and introduce a protocol for generating approximately Gaussian noise in a distributed manner. Compared to their protocol, our method of noise addition is considerably simpler and faster, and produces exactly instead of approximately Gaussian noise with negligible increase in noise level.
@cite_17
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How to achieve differential privacy in the distributed setting, where the dataset is distributed among the distrustful parties, is an important problem. We consider in what condition can a protocol inherit the differential privacy property of a function it computes. The heart of the problem is the secure multiparty computation of randomized function. A notion is introduced, which captures the key security problems when computing a randomized function from a deterministic one in the distributed setting. By this observation, a sufficient and necessary condition about computing a randomized function from a deterministic one is given. The above result can not only be used to determine whether a protocol computing differentially private function is secure, but also be used to construct secure one. Then we prove that the differential privacy property of a function can be inherited by the protocol computing it if the protocol privately computes it. A composition theorem of differentially private protocols is also presented. We also construct some protocols to generate random variate in the distributed setting, such as the uniform random variates and the inversion method. By using these fundamental protocols, we construct protocols of the Gaussian mechanism, the Laplace mechanism and the Exponential mechanism. Importantly, all these protocols satisfy obliviousness and so can be proved to be secure in a simulation based manner. We also provide a complexity bound of computing randomized function in the distribute setting. Finally, to show that our results are fundamental and powerful to multiparty differential privacy, we construct a differentially private empirical risk minimization protocol.