Privacy-preserving Data Sharing on Vertically Partitioned Data

In this work, we introduce a differentially private method for generating synthetic data from vertically partitioned data, \emph{i.e.}, where data of the same individuals is distributed across multiple data holders or parties. We present a differentially privacy stochastic gradient descent (DP-SGD) algorithm to train a mixture model over such partitioned data using variational inference. We modify a secure multiparty computation (MPC) framework to combine MPC with differential privacy (DP), in order to use differentially private MPC effectively to learn a probabilistic generative model under DP on such vertically partitioned data.
Assuming the mixture components contain no dependencies across different parties, the objective function can be factorized into a sum of products of the contributions calculated by the parties. Finally, MPC is used to compute the aggregate between the different contributions. Moreover, we rigorously define the privacy guarantees with respect to the different players in the system. To demonstrate the accuracy of our method, we run our algorithm on the Adult dataset from the UCI machine learning repository, where we obtain comparable results to the non-partitioned case.