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

In this paper, we focus on 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 theoretical analysis of its privacy and accuracy properties, offer guidance on setting hyperparameters, and show how to produce non-parametric, differentially private confidence intervals to accompany its point estimates.