# Differentially Private Verification of Distribution Properties

arXiv: https://arxiv.org/abs/2604.10819 · HTML: https://mlsanity.com/paper/2604.10819/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 60 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Builds on (most cited first, 19 of 19)

- [Hiding Among the Clones: A Simple and Nearly Optimal Analysis of Privacy Amplification by Shuffling](https://mlsanity.com/paper/2012.12803/) (2020)
- [Generalization in Adaptive Data Analysis and Holdout Reuse](https://mlsanity.com/paper/1506.02629/) (2015)
- [Reproducibility in Learning](https://mlsanity.com/paper/2201.08430/) (2022)
- [Stability is Stable: Connections between Replicability, Privacy, and Adaptive Generalization](https://mlsanity.com/paper/2303.12921/) (2023)
- [Optimal Testing for Properties of Distributions](https://mlsanity.com/paper/1507.05952/) (2015)
- [Max-Information, Differential Privacy, and Post-Selection Hypothesis Testing](https://mlsanity.com/paper/1604.03924/) (2016)
- [Differentially Private Testing of Identity and Closeness of Discrete Distributions](https://mlsanity.com/paper/1707.05128/) (2017)
- [Optimal Identity Testing with High Probability](https://mlsanity.com/paper/1708.02728/) (2017)
- [Testing probability distributions underlying aggregated data](https://mlsanity.com/paper/1402.3835/) (2014)
- [Collision-based Testers are Optimal for Uniformity and Closeness](https://mlsanity.com/paper/1611.03579/) (2016)
- [Private Identity Testing for High-Dimensional Distributions](https://mlsanity.com/paper/1905.11947/) (2019)
- [The Price of Tolerance in Distribution Testing](https://mlsanity.com/paper/2106.13414/) (2021)
- [Test without Trust: Optimal Locally Private Distribution Testing](https://mlsanity.com/paper/1808.02174/) (2018)
- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Generalized Uniformity Testing](https://mlsanity.com/paper/1708.04696/) (2017)
- [How to Verify Any (Reasonable) Distribution Property: Computationally Sound Argument Systems for Distributions](https://mlsanity.com/paper/2409.06594/) (2024)
- [Differentially Private Identity and Closeness Testing of Discrete Distributions](https://mlsanity.com/paper/1707.05497/) (2017)
- [Better Private Distribution Testing by Leveraging Unverified Auxiliary Data](https://mlsanity.com/paper/2503.14709/) (2025)
- [Optimal Prediction-Augmented Algorithms for Testing Independence of Distributions](https://mlsanity.com/paper/2603.04635/) (2026)

## Abstract (arXiv)

A recent line of work initiated by Chiesa and Gur and further developed by Herman and Rothblum investigates the sample and communication complexity of verifying properties of distributions with the assistance of a powerful, knowledgeable, but untrusted prover. In this work, we initiate the study of differentially private distribution property verification. After all, if we do not trust the prover to help us with verification, why should we trust it with our sensitive sample? We map a landscape of differentially private verification of properties of distributions. In the non-private case it is known that one-round private-coin protocols can have substantially lower complexity than public-coin (AM) protocols. In contrast, the possibility for improvement in differentially private interactive proofs depends on the privacy parameter regime and model. Drawing on connections between privacy and replicability and privacy amplification techniques in the literature we show: 1. There exists a reduction from any one-round (varepsilon,δ)-differentially private private-coin protocol to a differentially private AM protocol for the parameter regime varepsilon = O(1/√s) and δ= O(1/s5/2) with the same privacy and sample and communication complexities. In the local model, this is relaxed to varepsilon = O(1/√log s) 2. However, when the privacy guarantee is very relaxed (varepsilon ∈ Omega(log s)), private coins indeed reduce sample and communication complexities. We also obtain a computationally efficient Merlin-Arthur proof for privately testing whether samples are drawn from a product distribution and prove that its sample complexity is optimal up to a polylog N factor by reducing uniformity testing to independence testing with Boolean attributes and appealing to known lower bounds on sample complexity for private uniformity testing.