Analyzing the Differentially Private Theil-Sen Estimator for Simple Linear Regression
Authors: Jayshree Sarathy (Northeastern University), Salil Vadhan (Harvard University)
Volume: 2025
Issue: 1
Pages: 216–235
DOI: https://doi.org/10.56553/popets-2025-0013
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.
Keywords: differential privacy, linear regression, robust statistics, confidence intervals
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