# Analyzing the Differentially Private Theil-Sen Estimator for Simple Linear Regression

arXiv: https://arxiv.org/abs/2207.13289 · HTML: https://mlsanity.com/paper/2207.13289/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2022.

## Built on by (most cited first, 6 of 6)

- [Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation](https://mlsanity.com/paper/2402.13531/) (2024)
- [Improved Analysis of Sparse Linear Regression in Local Differential Privacy Model](https://mlsanity.com/paper/2310.07367/) (2023)
- [An Algorithm for Streaming Differentially Private Data](https://mlsanity.com/paper/2401.14577/) (2024)
- [Tukey Depth Mechanisms for Practical Private Mean Estimation](https://mlsanity.com/paper/2502.18698/) (2025)
- [Privately Estimating Black-Box Statistics](https://mlsanity.com/paper/2510.00322/) (2025)
- [The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2309.01243/) (2023)

## 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.