Differentially Private Identity and Closeness Testing of Discrete Distributions
This work addresses privacy-preserving statistical testing for discrete data, which is incremental by building on non-private methods with added privacy guarantees.
The paper tackled the problem of identity and closeness testing of discrete distributions while ensuring differential privacy, and the result showed that private testers can be nearly as sample-efficient as non-private ones, with experiments achieving small errors using sublinear sample sizes.
We investigate the problems of identity and closeness testing over a discrete population from random samples. Our goal is to develop efficient testers while guaranteeing Differential Privacy to the individuals of the population. We describe an approach that yields sample-efficient differentially private testers for these problems. Our theoretical results show that there exist private identity and closeness testers that are nearly as sample-efficient as their non-private counterparts. We perform an experimental evaluation of our algorithms on synthetic data. Our experiments illustrate that our private testers achieve small type I and type II errors with sample size sublinear in the domain size of the underlying distributions.