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

In this paper, we focus on differentially private point and interval estimators for simple linear regression. Motivated by recent work that highlights the strong empirical performance of a robust algorithm called $\texttt{DPTheilSen}$, we provide a theoretical analysis of its privacy and accuracy guarantees, offer guidance on setting hyperparameters, and show how to produce differentially private confidence intervals for the slope.