  We propose a categorical data synthesizer with a quantifiable disclosure
risk. Our algorithm, named Perturbed Gibbs Sampler, can handle high-dimensional
categorical data that are often intractable to represent as contingency tables.
The algorithm extends a multiple imputation strategy for fully synthetic data
by utilizing feature hashing and non-parametric distribution approximations.
California Patient Discharge data are used to demonstrate statistical
properties of the proposed synthesizing methodology. Marginal and conditional
distributions, as well as the coefficients of regression models built on the
synthesized data are compared to those obtained from the original data.
Intruder scenarios are simulated to evaluate disclosure risks of the
synthesized data from multiple angles. Limitations and extensions of the
proposed algorithm are also discussed.
