mlsanityData to 7 Oct 2026

Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain

arXiv 1803.02596 ↗First posted 7 Mar 2018stat.ML cs.LG stat.MEcited by 60

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Abstract (arXiv)

We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization error and estimation error, hence revealing the delicate price of differential privacy in statistical estimation and statistical learning. Moreover, we propose simple modifications of two existing DP algorithms: (a) posterior sampling, (b) sufficient statistics perturbation, and show that they can be upgraded into **adaptive** algorithms that are able to exploit data-dependent quantities and behave nearly optimally **for every instance**. Extensive experiments are conducted on both simulated data and real data, which conclude that both AdaOPS and AdaSSP outperform the existing techniques on nearly all 36 data sets that we test on.

Key facts. Cited by 60 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Mar 2018.

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Citing papers per year: 2021: 7; 2022: 8; 2023: 16; 2024: 13; 2025: 11; 2026: 5.

60 papers.

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  1. 2021Differential privacy and robust statistics in high dimensionscited by 64
  2. 2022Private Convex Optimization via Exponential Mechanismcited by 47
  3. 2021Differentially private inference via noisy optimizationcited by 27
  4. 2022DP-PCA: Statistically Optimal and Differentially Private PCAcited by 24
  5. 2023Score Attack: A Lower Bound Technique for Optimal Differentially Private Learningcited by 21
  6. 2022Easy Differentially Private Linear Regressioncited by 19
  7. 2022Differentially Private Generalized Linear Models Revisitedcited by 17
  8. 2023ReSQueing Parallel and Private Stochastic Convex Optimizationcited by 17
  9. 2024Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimationcited by 11
  10. 2022Differentially Private Regression with Unbounded Covariatescited by 10
  11. 2024Data-adaptive Differentially Private Prompt Synthesis for In-Context Learningcited by 10
  12. 2023Near Optimal Private and Robust Linear Regressioncited by 9
38 more
  1. 2024Neural Collapse Meets Differential Privacy: Curious Behaviors of NoisyGD with Near-perfect Representation Learningcited by 8
  2. 2021Non-parametric Differentially Private Confidence Intervals for the Mediancited by 7
  3. 2022Differentially Private Image Classification from Featurescited by 7
  4. 2024Insufficient Statistics Perturbation: Stable Estimators for Private Least Squarescited by 7
  5. 2021Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliabilitycited by 6
  6. 2022Generalized PTR: User-Friendly Recipes for Data-Adaptive Algorithms with Differential Privacycited by 6
  7. 2023Improved Differentially Private Regression via Gradient Boostingcited by 6
  8. 2023Private Learning with Public Featurescited by 6
  9. 2023Optimal Unbiased Randomizers for Regression with Label Differential Privacycited by 6
  10. 2023Better Private Linear Regression Through Better Private Feature Selectioncited by 5
  11. 2024Differentially Private Post-Processing for Fair Regressioncited by 5
  12. 2023Improved Analysis of Sparse Linear Regression in Local Differential Privacy Modelcited by 4
  13. 2024Private Regression via Data-Dependent Sufficient Statistic Perturbationcited by 4
  14. 2021Gaussian Processes with Differential Privacycited by 3
  15. 2021Differentially Private Nonparametric Regression Under a Growth Conditioncited by 3
  16. 2022Differentially Private Estimation via Statistical Depthcited by 3
  17. 2023Multi-Task Differential Privacy Under Distribution Skewcited by 3
  18. 2023Private Matrix Factorization with Public Item Featurescited by 3
  19. 2024Personalized Differential Privacy for Ridge Regressioncited by 3
  20. 2025On the Sample Complexity of Differentially Private Policy Optimizationcited by 3
  21. 2021High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guaranteescited by 2
  22. 2024Privacy Profiles for Private Selectioncited by 2
  23. 2024Convex Approximation of Two-Layer ReLU Networks for Hidden State Differential Privacycited by 2
  24. 2025Purifying Approximate Differential Privacy with Randomized Post-processingcited by 2
  25. 2025Sample-Optimal Private Regression in Polynomial Timecited by 2
  26. 2025The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketchescited by 2
  27. 2023Differentially Private Distributed Bayesian Linear Regression with MCMCcited by 1
  28. 2023The Relative Gaussian Mechanism and its Application to Private Gradient Descentcited by 1
  29. 2023On the Computational Complexity of Private High-dimensional Model Selectioncited by 1
  30. 2023Label Differential Privacy via Aggregationcited by 1
  31. 2024Better Locally Private Sparse Estimation Given Multiple Samples Per Usercited by 1
  32. 2024Distributed Differentially Private Data Analytics via Secure Sketchingcited by 1
  33. 2025Differentially Private Linear Regression and Synthetic Data Generation with Statistical Guaranteescited by 1
  34. 2025Differentially Private and Federated Structure Learning in Bayesian Networkscited by 1
  35. 2026Near-Optimal Private Linear Regression via Iterative Hessian Mixingcited by 1
  36. 2023PRIMO: Private Regression in Multiple Outcomescited by 0
  37. 2023The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learningcited by 0
  38. 2024Near-Optimal differentially private low-rank trace regression with guaranteed private initializationcited by 0

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