Really Useful Synthetic Data -- A Framework to Evaluate the Quality of Differentially Private Synthetic Data

Recent advances in generating synthetic data that allow to add principled ways of protecting privacy -- such as Differential Privacy -- are a crucial step in sharing statistical information in a privacy preserving way. But while the focus has been on privacy guarantees, the resulting private synthetic data is only useful if it still carries statistical information from the original data. To further optimise the inherent trade-off between data privacy and data quality, it is necessary to think closely about the latter. What is it that data analysts want? Acknowledging that data quality is a subjective concept, we develop a framework to evaluate the quality of differentially private synthetic data from an applied researcher's perspective. Data quality can be measured along two dimensions. First, quality of synthetic data can be evaluated against training data or against an underlying population. Second, the quality of synthetic data depends on general similarity of distributions or specific tasks such as inference or prediction. It is clear that accommodating all goals at once is a formidable challenge. We invite the academic community to jointly advance the privacy-quality frontier.