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We propose a method for the release of differentially private syntheticdatasets. In many contexts, data contain sensitive values which cannot bereleased in their original form in order to protect individuals' privacy.Synthetic data is a protection method that releases alternative values in placeof the original ones, and differential privacy (DP) is a formal guarantee forquantifying the privacy loss. We propose a method that maximizes thedistributional similarity of the synthetic data relative to the original datausing a measure known as the pMSE, while guaranteeing epsilon-differentialprivacy. Additionally, we relax common DP assumptions concerning thedistribution and boundedness of the original data. We prove theoretical resultsfor the privacy guarantee and provide simulations for the empirical failurerate of the theoretical results under typical computational limitations. Wealso give simulations for the accuracy of linear regression coefficientsgenerated from the synthetic data compared with the accuracy ofnon-differentially private synthetic data and other differentially privatemethods. Additionally, our theoretical results extend a prior result for thesensitivity of the Gini Index to include continuous predictors.

pMSE Mechanism: Differentially Private Synthetic Data with Maximal Distributional Similarity