# Differentially Private Confidence Intervals

arXiv: https://arxiv.org/abs/2001.02285 · HTML: https://mlsanity.com/paper/2001.02285/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2020.

## Built on by (most cited first, 20 of 20)

- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [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)
- [Privately Learning Mixtures of Axis-Aligned Gaussians](https://mlsanity.com/paper/2106.02162/) (2021)
- [A Bias-Accuracy-Privacy Trilemma for Statistical Estimation](https://mlsanity.com/paper/2301.13334/) (2023)
- [Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies](https://mlsanity.com/paper/2210.06140/) (2022)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [On the Statistical Complexity of Estimation and Testing under Privacy Constraints](https://mlsanity.com/paper/2210.02215/) (2022)
- [PLAN: Variance-Aware Private Mean Estimation](https://mlsanity.com/paper/2306.08745/) (2023)
- [A Polynomial Time, Pure Differentially Private Estimator for Binary Product Distributions](https://mlsanity.com/paper/2304.06787/) (2023)
- [DPM: Clustering Sensitive Data through Separation](https://mlsanity.com/paper/2307.02969/) (2023)
- [Private Geometric Median in Nearly-Linear Time](https://mlsanity.com/paper/2505.20189/) (2025)
- [Privately Estimating Black-Box Statistics](https://mlsanity.com/paper/2510.00322/) (2025)
- [Differentially Private E-Values](https://mlsanity.com/paper/2510.18654/) (2025)
- [Differentially Private Nonparametric Confidence Intervals Under Minimal Distributional Assumptions](https://mlsanity.com/paper/2511.01303/) (2025)
- [Instance-Specific Asymmetric Sensitivity in Differential Privacy](https://mlsanity.com/paper/2311.14681/) (2023)

## Abstract (arXiv)

Confidence intervals for the population mean of normally distributed data are some of the most standard statistical outputs one might want from a database. In this work we give practical differentially private algorithms for this task. We provide five algorithms and then compare them to each other and to prior work. We give concrete, experimental analysis of their accuracy and find that our algorithms provide much more accurate confidence intervals than prior work. For example, in one setting (with ε = 0.1 and n = 2782) our algorithm yields an interval that is only 1/15th the size of the standard set by prior work.