# Differentially Private Identity and Closeness Testing of Discrete Distributions

arXiv: https://arxiv.org/abs/1707.05497 · HTML: https://mlsanity.com/paper/1707.05497/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2017.

## Built on by (most cited first, 2 of 2)

- [Robust Kernel Hypothesis Testing under Data Corruption](https://mlsanity.com/paper/2405.19912/) (2024)
- [Differentially Private Verification of Distribution Properties](https://mlsanity.com/paper/2604.10819/) (2026)

## Abstract (arXiv)

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.