Boosting the Accuracy of Differentially-Private Queries Through Consistency

Recent differentially private query mechanisms offer strong privacy guarantees by adding noise to the query answer. For a single counting query, the technique is simple, accurate, and provides optimal utility. However, analysts typically wish to ask multiple queries. In this case, the optimal strategy is not apparent, and alternative query strategies can involve difficult trade-offs in accuracy, and may produce inconsistent answers. In this work we show that it is possible to significantly improve accuracy for a general class of histogram queries. Our approach carefully chooses a set of queries to evaluate, and then exploits consistency constraints that should hold over the noisy output. In a post-processing phase, we compute the consistent input most likely to have produced the noisy output. The final output is both private and consistent, but in addition, it is often much more accurate. We apply our techniques to real datasets and show they can be used for estimating the degree sequence of a graph with extreme precision, and for computing a histogram that can support arbitrary range queries accurately.