Analyzing the differentially private Theil-Sen estimator for simple linear regression
Publication information:
Sarathy, Jayshree, and Salil P. Vadhan. “Analyzing the Differentially Private Theil-Sen Estimator for Simple Linear Regression”. In 25th Privacy Enhancing Technologies Symposium (PoPETS ’25) . Washington, D.C.: Proceedings of the 25th Privacy Enhancing Technology Symposium (PoPETS ’25), volume 1, pages 216-235, 2025.
Abstract
Version History: Preliminary version presented as a poster at the 7th Workshop on the Theory and Practice of Differential Privacy (TPDP '21, July 2021) and posted as arXiv:2207.13289 [cs.CR]
Abstract: 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.