A Bayesian Nonparametric Approach to Differentially Private Data

Battiston, Marco and Ayed, Fadhel and Di Benedetto, Giuseppe (2020) A Bayesian Nonparametric Approach to Differentially Private Data. In: Privacy in Statistical Databases. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) . Springer, ESP, pp. 32-48. ISBN 9783030575205

Abstract

The protection of private and sensitive data is an important problem of increasing interest due to the vast amount of personal data collected. Differential Privacy is arguably the most dominant approach to address privacy protection, and is currently implemented in both industry and government. In a decentralized paradigm, the sensitive information belonging to each individual will be locally transformed by a known privacy-maintaining mechanism Q. The objective of differential privacy is to allow an analyst to recover the distribution of the raw data, or some functionals of it, while only having access to the transformed data. In this work, we propose a Bayesian nonparametric methodology to perform inference on the distribution of the sensitive data, reformulating the differentially private estimation problem as a latent variable Dirichlet Process mixture model. This methodology has the advantage that it can be applied to any mechanism Q and works as a “black box” procedure, being able to estimate the distribution and functionals thereof using the same MCMC draws and with very little tuning. Also, being a fully nonparametric procedure, it requires very little assumptions on the distribution of the raw data. For the most popular mechanisms Q, like Laplace and Gaussian, we describe efficient specialized MCMC algorithms and provide theoretical guarantees. Experiments on both synthetic and real dataset show a good performance of the proposed method.