Data Sharing via Differentially Private Coupled Matrix Factorization

We address the privacy-preserving data-sharing problem in a distributed multiparty setting. In this setting, each data site owns a distinct part of a dataset and the aim is to estimate the parameters of a statistical model conditioned on the complete data without any site revealing any information about the individuals in their own parts. The sites want to maximize the utility of the collective data analysis while providing privacy guarantees for their own portion of the data as well as for each participating individual. Our first contribution is to classify these different privacy requirements as (i) site-level and (ii) user-level differential privacy and present formal privacy guarantees for these two cases under the model of differential privacy. To satisfy a stronger form of differential privacy, we use a variant of differential privacy which is local differential privacy where the sensitive data is perturbed with a randomized response mechanism prior to the estimation. In this study, we assume that the data instances that are partitioned between several parties are arranged as matrices. A natural statistical model for this distributed scenario is coupled matrix factorization. We present two generic frameworks for privatizing Bayesian inference for coupled matrix factorization models that are able to guarantee proposed differential privacy notions based on the privacy requirements of the model. To privatize Bayesian inference, we first exploit the connection between differential privacy and sampling from a Bayesian posterior via stochastic gradient Langevin dynamics and then derive an efficient coupled matrix factorization method. In the local privacy context, we propose two models that have an additional privatization mechanism to achieve a stronger measure of privacy and introduce a Gibbs sampling based algorithm. We demonstrate that the proposed methods are able to provide good prediction accuracy on synthetic and real datasets while adhering to the introduced privacy constraints.