# A Polynomial Time, Pure Differentially Private Estimator for Binary Product Distributions

arXiv: https://arxiv.org/abs/2304.06787 · HTML: https://mlsanity.com/paper/2304.06787/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 71 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 30 of 53)

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (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)
- [Algorithmic Stability for Adaptive Data Analysis](https://mlsanity.com/paper/1511.02513/) (2015)
- [Fingerprinting Codes and the Price of Approximate Differential Privacy](https://mlsanity.com/paper/1311.3158/) (2013)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [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)
- [Differentially Private Release and Learning of Threshold Functions](https://mlsanity.com/paper/1504.07553/) (2015)
- [Private Hypothesis Selection](https://mlsanity.com/paper/1905.13229/) (2019)
- [Between Pure and Approximate Differential Privacy](https://mlsanity.com/paper/1501.06095/) (2015)
- [Differentially Private Assouad, Fano, and Le Cam](https://mlsanity.com/paper/2004.06830/) (2020)
- [Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation](https://mlsanity.com/paper/1906.02830/) (2019)
- [On Differentially Private Stochastic Convex Optimization with Heavy-tailed Data](https://mlsanity.com/paper/2010.11082/) (2020)
- [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)
- [Learning discrete distributions: user vs item-level privacy](https://mlsanity.com/paper/2007.13660/) (2020)
- [On the Sample Complexity of Privately Learning Unbounded High-Dimensional Gaussians](https://mlsanity.com/paper/2010.09929/) (2020)
- [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)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [Interactive Fingerprinting Codes and the Hardness of Preventing False Discovery](https://mlsanity.com/paper/1410.1228/) (2014)
- [Preventing False Discovery in Interactive Data Analysis is Hard](https://mlsanity.com/paper/1408.1655/) (2014)
- [Tight Lower Bounds for Differentially Private Selection](https://mlsanity.com/paper/1704.03024/) (2017)
- [FriendlyCore: Practical Differentially Private Aggregation](https://mlsanity.com/paper/2110.10132/) (2021)

## Built on by (most cited first, 5 of 5)

- [Sample-Optimal Locally Private Hypothesis Selection and the Provable Benefits of Interactivity](https://mlsanity.com/paper/2312.05645/) (2023)
- [Not All Learnable Distribution Classes are Privately Learnable](https://mlsanity.com/paper/2402.00267/) (2024)
- [About the Cost of Central Privacy in Density Estimation](https://mlsanity.com/paper/2306.14535/) (2023)
- [Learning with Differentially Private (Sliced) Wasserstein Gradients](https://mlsanity.com/paper/2502.01701/) (2025)
- [Privately Estimating Black-Box Statistics](https://mlsanity.com/paper/2510.00322/) (2025)

## Abstract (arXiv)

We present the first varepsilon-differentially private, computationally efficient algorithm that estimates the means of product distributions over 0,1d accurately in total-variation distance, whilst attaining the optimal sample complexity to within polylogarithmic factors. The prior work had either solved this problem efficiently and optimally under weaker notions of privacy, or had solved it optimally while having exponential running times.