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Finite Sample Differentially Private Confidence Intervals

arXiv 1711.03908 ↗First posted 10 Nov 2017cs.CR math.ST stat.THcited by 104

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Abstract (arXiv)

We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially private algorithms to estimate confidence intervals. Crucially, our algorithms guarantee a finite sample coverage, as opposed to an asymptotic coverage. Unlike most previous differentially private algorithms, we do not require the domain of the samples to be bounded. We also prove lower bounds on the expected size of any differentially private confidence set showing that our the parameters are optimal up to polylogarithmic factors.

Key facts. Cited by 104 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Nov 2017.

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Citing papers per year: 2021: 17; 2022: 19; 2023: 27; 2024: 16; 2025: 16; 2026: 9.

104 papers.

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  1. 2021Learning with User-Level Privacycited by 72
  2. 2021Robust and Differentially Private Mean Estimationcited by 66
  3. 2021Differential privacy and robust statistics in high dimensionscited by 64
  4. 2021Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanismcited by 50
  5. 2021Improved Rates for Differentially Private Stochastic Convex Optimization with Heavy-Tailed Datacited by 47
  6. 2022Robustness Implies Privacy in Statistical Estimationcited by 47
  7. 2021Covariance-Aware Private Mean Estimation Without Private Covariance Estimationcited by 46
  8. 2021Private and polynomial time algorithms for learning Gaussians and beyondcited by 39
  9. 2021Private Robust Estimation by Stabilizing Convex Relaxationscited by 38
  10. 2021FriendlyCore: Practical Differentially Private Aggregationcited by 34
  11. 2021A Private and Computationally-Efficient Estimator for Unbounded Gaussianscited by 34
  12. 2022New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemmacited by 33
38 more
  1. 2022When Privacy Meets Partial Information: A Refined Analysis of Differentially Private Banditscited by 28
  2. 2021Differentially private inference via noisy optimizationcited by 27
  3. 2021Optimal Rates of (Locally) Differentially Private Heavy-tailed Multi-Armed Banditscited by 25
  4. 2022Privacy Induces Robustness: Information-Computation Gaps and Sparse Mean Estimationcited by 25
  5. 2022Optimal and Differentially Private Data Acquisition: Central and Local Mechanismscited by 24
  6. 2022DP-PCA: Statistically Optimal and Differentially Private PCAcited by 24
  7. 2023Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributionscited by 22
  8. 2023Private estimation algorithms for stochastic block models and mixture modelscited by 21
  9. 2023Score Attack: A Lower Bound Technique for Optimal Differentially Private Learningcited by 21
  10. 2023Polynomial Time and Private Learning of Unbounded Gaussian Mixture Modelscited by 19
  11. 2021Private Prediction Setscited by 17
  12. 2021Differentially-Private Clustering of Easy Instancescited by 17
  13. 2023Better and Simpler Lower Bounds for Differentially Private Statistical Estimationcited by 17
  14. 2023Private Distribution Learning with Public Data: The View from Sample Compressioncited by 14
  15. 2021Privately Learning Mixtures of Axis-Aligned Gaussianscited by 13
  16. 2022Private High-Dimensional Hypothesis Testingcited by 12
  17. 2023A Bias-Accuracy-Privacy Trilemma for Statistical Estimationcited by 12
  18. 2022Differentially Private Regression with Unbounded Covariatescited by 10
  19. 2022Differentially Private Bootstrap: New Privacy Analysis and Inference Strategiescited by 10
  20. 2023Concentrated Differential Privacy for Banditscited by 10
  21. 2024Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraintscited by 10
  22. 2023Near Optimal Private and Robust Linear Regressioncited by 9
  23. 2024Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimescited by 9
  24. 2023Smooth Lower Bounds for Differentially Private Algorithms via Padding-and-Permuting Fingerprinting Codescited by 8
  25. 2023Mean Estimation with User-level Privacy under Data Heterogeneitycited by 8
  26. 2021Non-parametric Differentially Private Confidence Intervals for the Mediancited by 7
  27. 2021Generalization in the Face of Adaptivity: A Bayesian Perspectivecited by 7
  28. 2022Instance-Optimal Differentially Private Estimationcited by 7
  29. 2024Insufficient Statistics Perturbation: Stable Estimators for Private Least Squarescited by 7
  30. 2022Nonparametric extensions of randomized response for private confidence setscited by 6
  31. 2022On the Statistical Complexity of Estimation and Testing under Privacy Constraintscited by 6
  32. 2023On Private and Robust Banditscited by 6
  33. 2023PLAN: Variance-Aware Private Mean Estimationcited by 6
  34. 2023On the Complexity of Differentially Private Best-Arm Identification with Fixed Confidencecited by 6
  35. 2023Mean Estimation Under Heterogeneous Privacy Demandscited by 6
  36. 2024Federated Nonparametric Hypothesis Testing with Differential Privacy Constraints: Optimal Rates and Adaptive Testscited by 6
  37. 2024Dimension-free Private Mean Estimation for Anisotropic Distributionscited by 6
  38. 2023A Polynomial Time, Pure Differentially Private Estimator for Binary Product Distributionscited by 5

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