Analyzing the Differentially Private Theil-Sen Estimator for Simple Linear Regression
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Abstract (arXiv)
In this paper, we study differentially private point and confidence interval estimators for simple linear regression. Motivated by recent work that highlights the strong empirical performance of an algorithm based on robust statistics, DPTheilSen, we provide a rigorous, finite-sample analysis of its privacy and accuracy properties, offer guidance on setting hyperparameters, and show how to produce differentially private confidence intervals to accompany its point estimates.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Jul 2022.
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Citing papers per year: 2023: 2; 2024: 2; 2025: 2.
6 papers.
- 2024Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimationcited by 11
- 2023Improved Analysis of Sparse Linear Regression in Local Differential Privacy Modelcited by 4
- 2024An Algorithm for Streaming Differentially Private Datacited by 2
- 2025Tukey Depth Mechanisms for Practical Private Mean Estimationcited by 2
- 2023The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learningcited by 0
- 2025Privately Estimating Black-Box Statisticscited by 0
- 2025Privately Estimating Black-Box Statistics30 Sep 2025
- 2025Tukey Depth Mechanisms for Practical Private Mean Estimation25 Feb 2025
- 2024Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation21 Feb 2024
- 2024An Algorithm for Streaming Differentially Private Data26 Jan 2024
- 2023Improved Analysis of Sparse Linear Regression in Local Differential Privacy Model11 Oct 2023
- 2023The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning3 Sep 2023