mlsanityData to 7 Oct 2026

Near-Optimal Private Tests for Simple and MLR Hypotheses

arXiv 2601.21959 ↗First posted 29 Jan 2026stat.ML cs.LGcited by 0

Not on the map. Why?

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 28 of its 54 references that are in the map. First posted on arXiv 29 Jan 2026.

Builds on

28 of 54 references.

References · 28

  1. 2016Concentrated Differential Privacy: Simplifications, Extensions, and Lower Boundscited by 339
  2. 2016Robust Estimators in High Dimensions without the Computational Intractabilitycited by 209
  3. 2018Validating Bayesian Inference Algorithms with Simulation-Based Calibrationcited by 118
  4. 2017Finite Sample Differentially Private Confidence Intervalscited by 103
  5. 2020CoinPress: Practical Private Mean and Covariance Estimationcited by 74
  6. 2021Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanismcited by 50
  7. 2022Geographic Spines in the 2020 Census Disclosure Avoidance Systemcited by 42
  8. 2021Instance-optimal Mean Estimation Under Differential Privacycited by 37
  9. 2018The Structure of Optimal Private Tests for Simple Hypothesescited by 26
  10. 2016Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testingcited by 24
  11. 2021The Impact of the U.S. Census Disclosure Avoidance System on Redistricting and Voting Rights Analysiscited by 18
  12. 2021Unbiased Statistical Estimation and Valid Confidence Intervals Under Differential Privacycited by 15
16 more
  1. 2018Test without Trust: Optimal Locally Private Distribution Testingcited by 13
  2. 2019Differentially Private Nonparametric Hypothesis Testingcited by 12
  3. 2018Locally Private Hypothesis Testingcited by 11
  4. 2018Differentially Private Confidence Intervals for Empirical Risk Minimizationcited by 11
  5. 2017Local Private Hypothesis Testing: Chi-Square Testscited by 10
  6. 2023The Test of Tests: A Framework For Differentially Private Hypothesis Testingcited by 9
  7. 2021Canonical Noise Distributions and Private Hypothesis Testscited by 8
  8. 2021Non-parametric Differentially Private Confidence Intervals for the Mediancited by 7
  9. 2022Differentially Private Hypothesis Testing with the Subsampled and Aggregated Randomized Response Mechanismcited by 7
  10. 2023Simulation-based, Finite-sample Inference for Privatized Datacited by 7
  11. 2025Gaussian DP for Reporting Differential Privacy Guarantees in Machine Learningcited by 6
  12. 2022Log-Concave and Multivariate Canonical Noise Distributions for Differential Privacycited by 5
  13. 2019Differentially Private Inference for Binomial Datacited by 4
  14. 2020Testing goodness-of-fit and conditional independence with approximate co-sufficient samplingcited by 3
  15. 2022Differentially Private Kolmogorov-Smirnov-Type Testscited by 3
  16. 2025Optimal Debiased Inference on Privatized Data via Indirect Estimation and Parametric Bootstrapcited by 1

Built on by

Not cited yet.