# Near-Optimal Private Tests for Simple and MLR Hypotheses

arXiv: https://arxiv.org/abs/2601.21959 · HTML: https://mlsanity.com/paper/2601.21959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 28 of 28)

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [The Structure of Optimal Private Tests for Simple Hypotheses](https://mlsanity.com/paper/1811.11148/) (2018)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [The Impact of the U.S. Census Disclosure Avoidance System on Redistricting and Voting Rights Analysis](https://mlsanity.com/paper/2105.14197/) (2021)
- [Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacy](https://mlsanity.com/paper/2110.14465/) (2021)
- [Test without Trust: Optimal Locally Private Distribution Testing](https://mlsanity.com/paper/1808.02174/) (2018)
- [Differentially Private Nonparametric Hypothesis Testing](https://mlsanity.com/paper/1903.09364/) (2019)
- [Locally Private Hypothesis Testing](https://mlsanity.com/paper/1802.03441/) (2018)
- [Differentially Private Confidence Intervals for Empirical Risk Minimization](https://mlsanity.com/paper/1804.03794/) (2018)
- [Local Private Hypothesis Testing: Chi-Square Tests](https://mlsanity.com/paper/1709.07155/) (2017)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [Canonical Noise Distributions and Private Hypothesis Tests](https://mlsanity.com/paper/2108.04303/) (2021)
- [Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanism](https://mlsanity.com/paper/2208.06803/) (2022)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Simulation-based, Finite-sample Inference for Privatized Data](https://mlsanity.com/paper/2303.05328/) (2023)
- [Gaussian DP for Reporting Differential Privacy Guarantees in Machine Learning](https://mlsanity.com/paper/2503.10945/) (2025)
- [Log-Concave and Multivariate Canonical Noise Distributions for Differential Privacy](https://mlsanity.com/paper/2206.04572/) (2022)
- [Differentially Private Inference for Binomial Data](https://mlsanity.com/paper/1904.00459/) (2019)
- [Testing goodness-of-fit and conditional independence with approximate co-sufficient sampling](https://mlsanity.com/paper/2007.09851/) (2020)
- [Differentially Private Kolmogorov-Smirnov-Type Tests](https://mlsanity.com/paper/2208.06236/) (2022)
- [Optimal Debiased Inference on Privatized Data via Indirect Estimation and Parametric Bootstrap](https://mlsanity.com/paper/2507.10746/) (2025)

## Abstract (arXiv)

We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator with data-driven clamping bounds, whose population risk matches the private minimax rate up to logarithmic factors. Using this estimator, we construct private test statistics that achieve the same asymptotic relative efficiency as the non-private, most powerful tests while maintaining conservative type I error control. In addition to our theoretical results, our numerical experiments show that our private tests outperform competing DP methods and offer comparable power to the non-private most powerful tests, even at moderately small sample sizes and privacy loss budgets.