Differentially Private Medians and Interior Points for Non-Pathological Data

A statistical estimator is an algorithm that takes data drawn from an unknown distribution as input and tries to learn something about that distribution. While the input data is only a conduit for learning about the distribution, many statistical estimators also reveal a lot of information that is specific to the input data, which raises concerns about the privacy of people who contributed their data. In response, we can try to design estimators that are differentially private (DP) [DMNS06], which ensure that no attacker can infer much more about any person in the input data than they could have inferred in a hypothetical world where that person's data had never been collected. Differential privacy is a strong constraint that imposes significant costs even for very simple statistical estimation tasks. In this paper we focus on two such tasks: interior point estimation and median estimation. In the interior point problem, we have a distribution overR, and our goal is simply to output somepoint with inf support() sup support().