  We propose a method for the release of differentially private synthetic
datasets. In many contexts, data contain sensitive values which cannot be
released in their original form in order to protect individuals' privacy.
Synthetic data is a protection method that releases alternative values in place
of the original ones, and differential privacy (DP) is a formal guarantee for
quantifying the privacy loss. We propose a method that maximizes the
distributional similarity of the synthetic data relative to the original data
using a measure known as the pMSE, while guaranteeing epsilon-differential
privacy. Additionally, we relax common DP assumptions concerning the
distribution and boundedness of the original data. We prove theoretical results
for the privacy guarantee and provide simulations for the empirical failure
rate of the theoretical results under typical computational limitations. We
also give simulations for the accuracy of linear regression coefficients
generated from the synthetic data compared with the accuracy of
non-differentially private synthetic data and other differentially private
methods. Additionally, our theoretical results extend a prior result for the
sensitivity of the Gini Index to include continuous predictors.
