# Inference under Information Constraints III: Local Privacy Constraints

arXiv: https://arxiv.org/abs/2101.07981 · HTML: https://mlsanity.com/paper/2101.07981/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jan 2021.

## Built on by (most cited first, 13 of 13)

- [Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints](https://mlsanity.com/paper/2301.03566/) (2023)
- [Contraction of Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2210.13386/) (2022)
- [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022)
- [On the Statistical Complexity of Estimation and Testing under Privacy Constraints](https://mlsanity.com/paper/2210.02215/) (2022)
- [Federated Nonparametric Hypothesis Testing with Differential Privacy Constraints: Optimal Rates and Adaptive Tests](https://mlsanity.com/paper/2406.06749/) (2024)
- [Continual Mean Estimation Under User-Level Privacy](https://mlsanity.com/paper/2212.09980/) (2022)
- [Private Statistical Estimation of Many Quantiles](https://mlsanity.com/paper/2302.06943/) (2023)
- [Sample-Optimal Locally Private Hypothesis Selection and the Provable Benefits of Interactivity](https://mlsanity.com/paper/2312.05645/) (2023)
- [Private independence testing across two parties](https://mlsanity.com/paper/2207.03652/) (2022)
- [About the Cost of Central Privacy in Density Estimation](https://mlsanity.com/paper/2306.14535/) (2023)
- [Statistical Inference with Limited Memory: A Survey](https://mlsanity.com/paper/2312.15225/) (2023)
- [Uniformity Testing in the Shuffle Model: Simpler, Better, Faster](https://mlsanity.com/paper/2108.08987/) (2021)
- [Sample-optimal learning of quantum states using gentle measurements](https://mlsanity.com/paper/2505.24587/) (2025)

## Abstract (arXiv)

We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform the tests. Under the notion of local differential privacy, we propose simple, sample-optimal, and communication-efficient protocols for these two questions in the noninteractive setting, where in addition users may or may not share a common random seed. In particular, we show that the availability of shared (public) randomness greatly reduces the sample complexity. Underlying our public-coin protocols are privacy-preserving mappings which, when applied to the samples, minimally contract the distance between their respective probability distributions.