Integrating Differential Privacy in the Statistical Disclosure Control Tool-Kit for Synthetic Data Production

Abstract

A standard approach in the statistical disclosure control tool-kit for producing synthetic data is the procedure based on multivariate sequential chained-equation regression models where each successive regression includes variables from the preceding regressions. The models depend on conditional Bayesian posterior distributions and can handle continuous, binary and categorical variables. Synthetic data are generated by drawing random values from the corresponding predictive distributions. Multiple copies of the synthetic data are generated and inference carried out on each of the data sets with results combined for point and variance estimates under well-established combination rules. In this paper, we investigate whether algorithms and mechanisms found in the differential privacy literature can be added to the synthetic data production process to raise the privacy standards used at National Statistical Institutes. In particular, we focus on a differentially private functional mechanism of adding random noise to the estimating equations of the regression models. We also incorporate regularization in the OLS linear models (ridge regression) to compensate for noisy estimating equations and bound the global sensitivity. We evaluate the standard and modified multivariate sequential chained-equation regression approach for producing synthetic data in a small-scale simulation study.