Private Statistical Estimation via Truncation
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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.
Key facts. Cited by 1 paper 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
29 of 58 references.
References · 29
- 2016Deep Learning with Differential Privacycited by 2,728
- 2014RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Responsecited by 272
- 2020Private Stochastic Convex Optimization: Optimal Rates in Linear Timecited by 153
- 2017Finite Sample Differentially Private Confidence Intervalscited by 104
- 2020CoinPress: Practical Private Mean and Covariance Estimationcited by 74
- 2017Sub-sampled Cubic Regularization for Non-convex Optimizationcited by 63
- 2021Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanismcited by 50
- 2022Robustness Implies Privacy in Statistical Estimationcited by 47
- 2020On the Sample Complexity of Privately Learning Unbounded High-Dimensional Gaussianscited by 41
- 2021Private and polynomial time algorithms for learning Gaussians and beyondcited by 39
- 2015Differentially Private Ordinary Least Squarescited by 36
- 2015Simultaneous Private Learning of Multiple Conceptscited by 34
17 more
- 2022New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemmacited by 33
- 2018Efficient Statistics, in High Dimensions, from Truncated Samplescited by 28
- 2016Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testingcited by 24
- 2020Computationally and Statistically Efficient Truncated Regressioncited by 24
- 2019Efficient Truncated Statistics with Unknown Truncationcited by 22
- 2016Locating a Small Cluster Privatelycited by 20
- 2018Differentially Private Bayesian Inference for Exponential Familiescited by 18
- 2023Better and Simpler Lower Bounds for Differentially Private Statistical Estimationcited by 17
- 2020Truncated Linear Regression in High Dimensionscited by 13
- 2019Optimal Learning of Mallows Block Modelcited by 12
- 2021A Computationally Efficient Method for Learning Exponential Family Distributionscited by 10
- 2022Efficient Truncated Linear Regression with Unknown Noise Variancecited by 10
- 2021Learning from Censored and Dependent Data: The case of Linear Dynamicscited by 9
- 2024Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimescited by 9
- 2022Instance-Optimal Differentially Private Estimationcited by 7
- 2024Efficient Statistics With Unknown Truncation, Polynomial Time Algorithms, Beyond Gaussianscited by 7
- 2023Convergence rate analysis of a Dykstra-type projection algorithmcited by 1
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Citing papers per year: 2026: 1.
1 paper.
- 2026Mean Testing under Truncation beyond Gaussiancited by 0
- 2026Mean Testing under Truncation beyond Gaussian2 May 2026