  Synthetic data generation methods, and in particular, private synthetic data
generation methods, are gaining popularity as a means to make copies of
sensitive databases that can be shared widely for research and data analysis.
Some of the fundamental operations in data analysis include analyzing
aggregated statistics, e.g., count, sum, or median, on a subset of data
satisfying some conditions. When synthetic data is generated, users may be
interested in knowing if their aggregated queries generating such statistics
can be reliably answered on the synthetic data, for instance, to decide if the
synthetic data is suitable for specific tasks. However, the standard data
generation systems do not provide "per-query" quality guarantees on the
synthetic data, and the users have no way of knowing how much the aggregated
statistics on the synthetic data can be trusted. To address this problem, we
present a novel framework named DP-PQD (differentially-private per-query
decider) to detect if the query answers on the private and synthetic datasets
are within a user-specified threshold of each other while guaranteeing
differential privacy. We give a suite of private algorithms for per-query
deciders for count, sum, and median queries, analyze their properties, and
evaluate them experimentally.
