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

arXiv:2207.13289v2 Announce Type: replace
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.

accuracy algorithm analysis arxiv cs.cr linear performance point privacy private sample simple stat.ap statistics study work