# A Primer on Private Statistics

arXiv: https://arxiv.org/abs/2005.00010 · HTML: https://mlsanity.com/paper/2005.00010/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2020.

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

- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Composition of Differential Privacy & Privacy Amplification by Subsampling](https://mlsanity.com/paper/2210.00597/) (2022)
- [Private and polynomial time algorithms for learning Gaussians and beyond](https://mlsanity.com/paper/2111.11320/) (2021)
- [The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning](https://mlsanity.com/paper/2203.03761/) (2022)
- [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)
- [Faster Rates of Convergence to Stationary Points in Differentially Private Optimization](https://mlsanity.com/paper/2206.00846/) (2022)
- [Differentially Private Quantiles](https://mlsanity.com/paper/2102.08244/) (2021)
- [Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions](https://mlsanity.com/paper/2301.12250/) (2023)
- [Better and Simpler Lower Bounds for Differentially Private Statistical Estimation](https://mlsanity.com/paper/2310.06289/) (2023)
- [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 Sampling from Distributions](https://mlsanity.com/paper/2211.08193/) (2022)
- [Instance-Optimal Differentially Private Estimation](https://mlsanity.com/paper/2210.15819/) (2022)
- [Mean Estimation Under Heterogeneous Privacy: Some Privacy Can Be Free](https://mlsanity.com/paper/2305.09668/) (2023)
- [Mean Estimation Under Heterogeneous Privacy Demands](https://mlsanity.com/paper/2310.13137/) (2023)
- [Public-data Assisted Private Stochastic Optimization: Power and Limitations](https://mlsanity.com/paper/2403.03856/) (2024)
- [Continual Mean Estimation Under User-Level Privacy](https://mlsanity.com/paper/2212.09980/) (2022)
- [A Polynomial Time, Pure Differentially Private Estimator for Binary Product Distributions](https://mlsanity.com/paper/2304.06787/) (2023)
- [Private Federated Learning with Autotuned Compression](https://mlsanity.com/paper/2307.10999/) (2023)
- [Distribution Learnability and Robustness](https://mlsanity.com/paper/2406.17814/) (2024)
- [Not All Learnable Distribution Classes are Privately Learnable](https://mlsanity.com/paper/2402.00267/) (2024)
- [Differentially Private Optimization with Sparse Gradients](https://mlsanity.com/paper/2404.10881/) (2024)
- [Differentially Private Prototypes for Imbalanced Transfer Learning](https://mlsanity.com/paper/2406.08039/) (2024)
- [Differentially Private Ensemble Classifiers for Data Streams](https://mlsanity.com/paper/2112.04640/) (2021)
- [Privacy Preserving Adaptive Experiment Design](https://mlsanity.com/paper/2401.08224/) (2024)
- [How Private is Your Attention? Bridging Privacy with In-Context Learning](https://mlsanity.com/paper/2504.16000/) (2025)
- [Beyond ATE: Multi-Criteria Design for A/B Testing](https://mlsanity.com/paper/2509.05864/) (2025)
- [Query-Efficient Locally Private Hypothesis Selection via the Scheffe Graph](https://mlsanity.com/paper/2509.16180/) (2025)
- [Sequential Auditing for f-Differential Privacy](https://mlsanity.com/paper/2602.06518/) (2026)

## Abstract (arXiv)

Differentially private statistical estimation has seen a flurry of developments over the last several years. Study has been divided into two schools of thought, focusing on empirical statistics versus population statistics. We suggest that these two lines of work are more similar than different by giving examples of methods that were initially framed for empirical statistics, but can be applied just as well to population statistics. We also provide a thorough coverage of recent work in this area.