Pure differential privacy for rectangle queries via private partitions

Abstract

We consider the task of data analysis with pure differential privacy. We construct new and improved mechanisms for statistical release of interval and rectangle queries. We also obtain a new algorithm for counting over a data stream under continual observation, whose error has optimal dependence on the data stream’s length. A central ingredient in all of these result is a differentially private partition mechanism. Given set of data items drawn from a large universe, this mechanism outputs a partition of the universe into a small number of segments, each of which contain only a few of the data items.