Maximizing Utility for Vector-weighted Pseudo Posterior Mechanisms under Differential Privacy

Abstract

The risk-weighted pseudo posterior mechanism provides a practical framework for privacy protection that takes advantage of the availability of posterior sampling approaches, creating a synthesizer for microdata dissemination. The flexibility of the approach lies in the user-specification of the individualized risks and the mapping of risks to weights. However, this raises the question of which weighting approach is optimal. In this work, we develop a recursive approach to algorithmically induce an optimal weighting strategy given an initial suboptimal strategy. This ` re-weighting' strategy applies to any vector-weighted pseudo posterior mechanism under which a vector of observation-indexed weights are used to downweight likelihood contributions for high disclosure risk records. We demonstrate our method on two different vector-weighted schemes that target high-risk records (one close to optimal and one not). Our new method for constructing record-indexed downweighting maximizes the data utility under any privacy budget for the vector-weighted synthesizers by adjusting the by-record weights, such that their individual risk contributions (e.g. Lipschitz bounds) approach the risk bound for the entire database. Our method achieves an epsilon-asymptotic differential privacy (aDP) guarantee, globally, over the space of databases. We illustrate our methods using simulated highly skewed count data and compare the results to a scalar-weighted synthesizer under the popular Exponential Mechanism (EM). We also apply our methods to a sample of the Survey of Doctorate Recipients and demonstrate the practicality of our methods.