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Electronic health records (EHR) often contain sensitive medical informationabout individual patients, posing significant limitations to sharing orreleasing EHR data for downstream learning and inferential tasks. We usenormalizing flows (NF), a family of deep generative models, to estimate theprobability density of a dataset with differential privacy (DP) guarantees,from which privacy-preserving synthetic data are generated. We apply thetechnique to an EHR dataset containing patients with pulmonary hypertension. Weassess the learning and inferential utility of the synthetic data by comparingthe accuracy in the prediction of the hypertension status and variationalposterior distribution of the parameters of a physics-based model. In addition,we use a simulated dataset from a nonlinear model to compare the results fromvariational inference (VI) based on privacy-preserving synthetic data, andprivacy-preserving VI obtained from directly privatizing NFs for VI with DPguarantees given the original non-private dataset. The results suggest thatsynthetic data generated through differentially private density estimation withNF can yield good utility at a reasonable privacy cost. We also show that VIobtained from differentially private NF based on the free energy bound loss mayproduce variational approximations with significantly altered correlationstructure, and loss formulations based on alternative dissimilarity metricsbetween two distributions might provide improved results.

Differentially Private Normalizing Flows for Density Estimation, Data  Synthesis, and Variational Inference with Application to Electronic Health  Records