# Instance-Optimal Differentially Private Estimation

arXiv: https://arxiv.org/abs/2210.15819 · HTML: https://mlsanity.com/paper/2210.15819/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 28 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [Fingerprinting Codes and the Price of Approximate Differential Privacy](https://mlsanity.com/paper/1311.3158/) (2013)
- [Private PAC learning implies finite Littlestone dimension](https://mlsanity.com/paper/1806.00949/) (2018)
- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [Simultaneous Private Learning of Multiple Concepts](https://mlsanity.com/paper/1511.08552/) (2015)
- [Tight Lower Bounds for Differentially Private Selection](https://mlsanity.com/paper/1704.03024/) (2017)
- [The Power of Factorization Mechanisms in Local and Central Differential Privacy](https://mlsanity.com/paper/1911.08339/) (2019)
- [A Primer on Private Statistics](https://mlsanity.com/paper/2005.00010/) (2020)
- [The Structure of Optimal Private Tests for Simple Hypotheses](https://mlsanity.com/paper/1811.11148/) (2018)
- [Differentially Private Testing of Identity and Closeness of Discrete Distributions](https://mlsanity.com/paper/1707.05128/) (2017)
- [Near Instance-Optimality in Differential Privacy](https://mlsanity.com/paper/2005.10630/) (2020)
- [Recursive Mechanism: Towards Node Differential Privacy and Unrestricted Joins [Full Version, Draft 0.1]](https://mlsanity.com/paper/1304.4795/) (2013)
- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)

## Built on by (most cited first, 7 of 7)

- [Mean Estimation with User-level Privacy under Data Heterogeneity](https://mlsanity.com/paper/2307.15835/) (2023)
- [General Gaussian Noise Mechanisms and Their Optimality for Unbiased Mean Estimation](https://mlsanity.com/paper/2301.13850/) (2023)
- [Subset-Based Instance Optimality in Private Estimation](https://mlsanity.com/paper/2303.01262/) (2023)
- [Locally Optimal Private Sampling: Beyond the Global Minimax](https://mlsanity.com/paper/2510.09485/) (2025)
- [Private Statistical Estimation via Truncation](https://mlsanity.com/paper/2505.12541/) (2025)
- [Optimal Rates for Differentially Private Hypothesis Testing with E-values](https://mlsanity.com/paper/2605.28952/) (2026)
- [Instance-Specific Asymmetric Sensitivity in Differential Privacy](https://mlsanity.com/paper/2311.14681/) (2023)

## Abstract (arXiv)

In this work, we study local minimax convergence estimation rates subject to ε-differential privacy. Unlike worst-case rates, which may be conservative, algorithms that are locally minimax optimal must adapt to easy instances of the problem. We construct locally minimax differentially private estimators for one-parameter exponential families and estimating the tail rate of a distribution. In these cases, we show that optimal algorithms for simple hypothesis testing, namely the recent optimal private testers of Canonne et al. (2019), directly inform the design of locally minimax estimation algorithms.