# Finite Sample Differentially Private Confidence Intervals

arXiv: https://arxiv.org/abs/1711.03908 · HTML: https://mlsanity.com/paper/1711.03908/

## Key facts

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

## Built on by (most cited first, 30 of 104)

- [Learning with User-Level Privacy](https://mlsanity.com/paper/2102.11845/) (2021)
- [Robust and Differentially Private Mean Estimation](https://mlsanity.com/paper/2102.09159/) (2021)
- [Differential privacy and robust statistics in high dimensions](https://mlsanity.com/paper/2111.06578/) (2021)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Improved Rates for Differentially Private Stochastic Convex Optimization with Heavy-Tailed Data](https://mlsanity.com/paper/2106.01336/) (2021)
- [Robustness Implies Privacy in Statistical Estimation](https://mlsanity.com/paper/2212.05015/) (2022)
- [Covariance-Aware Private Mean Estimation Without Private Covariance Estimation](https://mlsanity.com/paper/2106.13329/) (2021)
- [Private and polynomial time algorithms for learning Gaussians and beyond](https://mlsanity.com/paper/2111.11320/) (2021)
- [Private Robust Estimation by Stabilizing Convex Relaxations](https://mlsanity.com/paper/2112.03548/) (2021)
- [FriendlyCore: Practical Differentially Private Aggregation](https://mlsanity.com/paper/2110.10132/) (2021)
- [A Private and Computationally-Efficient Estimator for Unbounded Gaussians](https://mlsanity.com/paper/2111.04609/) (2021)
- [New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemma](https://mlsanity.com/paper/2205.08532/) (2022)
- [When Privacy Meets Partial Information: A Refined Analysis of Differentially Private Bandits](https://mlsanity.com/paper/2209.02570/) (2022)
- [Differentially private inference via noisy optimization](https://mlsanity.com/paper/2103.11003/) (2021)
- [Optimal Rates of (Locally) Differentially Private Heavy-tailed Multi-Armed Bandits](https://mlsanity.com/paper/2106.02575/) (2021)
- [Privacy Induces Robustness: Information-Computation Gaps and Sparse Mean Estimation](https://mlsanity.com/paper/2211.00724/) (2022)
- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions](https://mlsanity.com/paper/2301.12250/) (2023)
- [Private estimation algorithms for stochastic block models and mixture models](https://mlsanity.com/paper/2301.04822/) (2023)
- [Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning](https://mlsanity.com/paper/2303.07152/) (2023)
- [Polynomial Time and Private Learning of Unbounded Gaussian Mixture Models](https://mlsanity.com/paper/2303.04288/) (2023)
- [Private Prediction Sets](https://mlsanity.com/paper/2102.06202/) (2021)
- [Differentially-Private Clustering of Easy Instances](https://mlsanity.com/paper/2112.14445/) (2021)
- [Better and Simpler Lower Bounds for Differentially Private Statistical Estimation](https://mlsanity.com/paper/2310.06289/) (2023)
- [Private Distribution Learning with Public Data: The View from Sample Compression](https://mlsanity.com/paper/2308.06239/) (2023)
- [Privately Learning Mixtures of Axis-Aligned Gaussians](https://mlsanity.com/paper/2106.02162/) (2021)
- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [A Bias-Accuracy-Privacy Trilemma for Statistical Estimation](https://mlsanity.com/paper/2301.13334/) (2023)
- [Differentially Private Regression with Unbounded Covariates](https://mlsanity.com/paper/2202.11199/) (2022)

## 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.