Privacy-preserving Data Sharing on Vertically Partitioned Data

In this work, we present a method for differentially private data sharing by training a mixture model on vertically partitioned data, where each party holds different features for the same set of individuals. We use secure multi-party computation (MPC) to combine the contribution of the data from the parties to train the model. We apply the differentially private variational inference (DPVI) for learning the model. Assuming the mixture components contain no dependencies across different parties, the objective function can be factorized into a sum of products of individual components of each party. Therefore, each party can calculate its shares on its own without the use of MPC. Then MPC is only needed to get the product between the different shares and add the noise. Applying the method to demographic data from the US Census, we obtain comparable accuracy to the non-partitioned case with approximately 20-fold increase in computing time.