mlsanityData to 14 Oct 2026

Easy Differentially Private Linear Regression

arXiv 2208.07353 ↗First posted 15 Aug 2022cs.LG cs.CRcited by 19

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Abstract (arXiv)

Linear regression is a fundamental tool for statistical analysis. This has motivated the development of linear regression methods that also satisfy differential privacy and thus guarantee that the learned model reveals little about any one data point used to construct it. However, existing differentially private solutions assume that the end user can easily specify good data bounds and hyperparameters. Both present significant practical obstacles. In this paper, we study an algorithm which uses the exponential mechanism to select a model with high Tukey depth from a collection of non-private regression models. Given n samples of d-dimensional data used to train m models, we construct an efficient analogue using an approximate Tukey depth that runs in time O(d2n + dmlog(m)). We find that this algorithm obtains strong empirical performance in the data-rich setting with no data bounds or hyperparameter selection required.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 15 of its 41 references that are in the map. First posted on arXiv 15 Aug 2022.

Builds on

15 of 41 references.

References · 15

  1. 2016Deep Learning with Differential Privacycited by 2,728
  2. 2019Private Stochastic Convex Optimization with Optimal Ratescited by 186
  3. 2021Hyperparameter Tuning with Renyi Differential Privacycited by 104
  4. 2018Private Selection from Private Candidatescited by 75
  5. 2021Robust and Differentially Private Mean Estimationcited by 66
  6. 2021Differential privacy and robust statistics in high dimensionscited by 64
  7. 2018Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domaincited by 61
  8. 2021Covariance-Aware Private Mean Estimation Without Private Covariance Estimationcited by 46
  9. 2020Differentially Private Simple Linear Regressioncited by 34
  10. 2019Private Center Points and Learning of Halfspacescited by 14
  11. 2022Differentially Private Regression with Unbounded Covariatescited by 10
  12. 2021Differentially private depth functions and their associated medianscited by 7
3 more
  1. 2020Duff: A Dataset-Distance-Based Utility Function Family for the Exponential Mechanismcited by 6
  2. 2020How to Find a Point in the Convex Hull Privatelycited by 5
  3. 2022Differentially Private Estimation via Statistical Depthcited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 5; 2024: 7; 2025: 4; 2026: 3.

19 papers.

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  1. 2024Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimationcited by 12
  2. 2023Near Optimal Private and Robust Linear Regressioncited by 9
  3. 2023Improved Differentially Private Regression via Gradient Boostingcited by 6
  4. 2023Better Private Linear Regression Through Better Private Feature Selectioncited by 5
  5. 2024Private Regression via Data-Dependent Sufficient Statistic Perturbationcited by 4
  6. 2024Convex Approximation of Two-Layer ReLU Networks for Hidden State Differential Privacycited by 2
  7. 2025Tukey Depth Mechanisms for Practical Private Mean Estimationcited by 2
  8. 2023Label Differential Privacy via Aggregationcited by 1
  9. 2024Better Locally Private Sparse Estimation Given Multiple Samples Per Usercited by 1
  10. 2025Improved subsample-and-aggregate via the private modified winsorized meancited by 1
  11. 2025Differentially Private Linear Regression and Synthetic Data Generation with Statistical Guaranteescited by 1
  12. 2026Near-Optimal Private Linear Regression via Iterative Hessian Mixingcited by 1
7 more
  1. 2023The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learningcited by 0
  2. 2024DP-KAN: Differentially Private Kolmogorov-Arnold Networkscited by 0
  3. 2024Testing Credibility of Public and Private Surveys through the Lens of Regressioncited by 0
  4. 2024Private Linear Regression with Differential Privacy and PAC Privacycited by 0
  5. 2025Differentially Private Two-Stage Gradient Descent for Instrumental Variable Regressioncited by 0
  6. 2026Refined Differentially Private Linear Regression via Extension of a Free Lunch Resultcited by 0
  7. 2026Enhancing Differentially Private Mechanisms via Empirical Bayescited by 0