# Private Statistical Estimation via Truncation

arXiv: https://arxiv.org/abs/2505.12541 · HTML: https://mlsanity.com/paper/2505.12541/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 58 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 29 of 29)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [Private Stochastic Convex Optimization: Optimal Rates in Linear Time](https://mlsanity.com/paper/2005.04763/) (2020)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Sub-sampled Cubic Regularization for Non-convex Optimization](https://mlsanity.com/paper/1705.05933/) (2017)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Robustness Implies Privacy in Statistical Estimation](https://mlsanity.com/paper/2212.05015/) (2022)
- [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)
- [Differentially Private Ordinary Least Squares](https://mlsanity.com/paper/1507.02482/) (2015)
- [Simultaneous Private Learning of Multiple Concepts](https://mlsanity.com/paper/1511.08552/) (2015)
- [New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemma](https://mlsanity.com/paper/2205.08532/) (2022)
- [Efficient Statistics, in High Dimensions, from Truncated Samples](https://mlsanity.com/paper/1809.03986/) (2018)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [Computationally and Statistically Efficient Truncated Regression](https://mlsanity.com/paper/2010.12000/) (2020)
- [Efficient Truncated Statistics with Unknown Truncation](https://mlsanity.com/paper/1908.01034/) (2019)
- [Locating a Small Cluster Privately](https://mlsanity.com/paper/1604.05590/) (2016)
- [Differentially Private Bayesian Inference for Exponential Families](https://mlsanity.com/paper/1809.02188/) (2018)
- [Better and Simpler Lower Bounds for Differentially Private Statistical Estimation](https://mlsanity.com/paper/2310.06289/) (2023)
- [Truncated Linear Regression in High Dimensions](https://mlsanity.com/paper/2007.14539/) (2020)
- [Optimal Learning of Mallows Block Model](https://mlsanity.com/paper/1906.01009/) (2019)
- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [Efficient Truncated Linear Regression with Unknown Noise Variance](https://mlsanity.com/paper/2208.12042/) (2022)
- [Learning from Censored and Dependent Data: The case of Linear Dynamics](https://mlsanity.com/paper/2104.05087/) (2021)
- [Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes](https://mlsanity.com/paper/2404.17714/) (2024)
- [Instance-Optimal Differentially Private Estimation](https://mlsanity.com/paper/2210.15819/) (2022)
- [Efficient Statistics With Unknown Truncation, Polynomial Time Algorithms, Beyond Gaussians](https://mlsanity.com/paper/2410.01656/) (2024)
- [Convergence rate analysis of a Dykstra-type projection algorithm](https://mlsanity.com/paper/2301.03026/) (2023)

## Built on by (most cited first, 1 of 1)

- [Mean Testing under Truncation beyond Gaussian](https://mlsanity.com/paper/2605.01335/) (2026)

## Abstract (arXiv)

We introduce a novel framework for differentially private (DP) statistical estimation via data truncation, addressing a key challenge in DP estimation when the data support is unbounded. Traditional approaches rely on problem-specific sensitivity analysis, limiting their applicability. By leveraging techniques from truncated statistics, we develop computationally efficient DP estimators for exponential family distributions, including Gaussian mean and covariance estimation, achieving near-optimal sample complexity. Previous works on exponential families only consider bounded or one-dimensional families. Our approach mitigates sensitivity through truncation while carefully correcting for the introduced bias using maximum likelihood estimation and DP stochastic gradient descent. Along the way, we establish improved uniform convergence guarantees for the log-likelihood function of exponential families, which may be of independent interest. Our results provide a general blueprint for DP algorithm design via truncated statistics.