# Locally Private Hypothesis Testing

arXiv: https://arxiv.org/abs/1802.03441 · HTML: https://mlsanity.com/paper/1802.03441/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2018.

## Built on by (most cited first, 11 of 11)

- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints](https://mlsanity.com/paper/2301.03566/) (2023)
- [Federated Nonparametric Hypothesis Testing with Differential Privacy Constraints: Optimal Rates and Adaptive Tests](https://mlsanity.com/paper/2406.06749/) (2024)
- ["You Can't Fix What You Can't Measure": Privately Measuring Demographic Performance Disparities in Federated Learning](https://mlsanity.com/paper/2206.12183/) (2022)
- [Private Sequential Hypothesis Testing for Statisticians: Privacy, Error Rates, and Sample Size](https://mlsanity.com/paper/2204.04597/) (2022)
- [Private independence testing across two parties](https://mlsanity.com/paper/2207.03652/) (2022)
- [Optimal Algorithms for Augmented Testing of Discrete Distributions](https://mlsanity.com/paper/2412.00974/) (2024)
- [On the Computational Complexity of Private High-dimensional Model Selection](https://mlsanity.com/paper/2310.07852/) (2023)
- [Uniformity Testing in the Shuffle Model: Simpler, Better, Faster](https://mlsanity.com/paper/2108.08987/) (2021)
- [Query-Efficient Locally Private Hypothesis Selection via the Scheffe Graph](https://mlsanity.com/paper/2509.16180/) (2025)
- [Near-Optimal Private Tests for Simple and MLR Hypotheses](https://mlsanity.com/paper/2601.21959/) (2026)

## Abstract (arXiv)

We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism (Warner, 1965, Kasiviswanathan et al, 2008) and the newer (non-symmetric) mechanisms (Bassily and Smith, 2015, Bassily et al, 2017). First, we study the general framework of mapping each user's type into a signal and show that the problem of finding the maximum-likelihood distribution over the signals is feasible. Then we discuss the randomized-response mechanism and show that, in essence, it maps the null- and alternative-hypotheses onto new sets, an affine translation of the original sets. We then give sample complexity bounds for identity and independence testing under randomized-response. We then move to the newer non-symmetric mechanisms and show that there too the problem of finding the maximum-likelihood distribution is feasible. Under the mechanism of Bassily et al (2007) we give identity and independence testers with better sample complexity than the testers in the symmetric case, and we also propose a chi2-based identity tester which we investigate empirically.