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

TL;DR

This paper rigorously analyzes the privacy and accuracy of a differentially private Theil-Sen estimator for simple linear regression, providing guidance on hyperparameter tuning and confidence interval construction.

Contribution

It offers a finite-sample analysis of DPTheilSen, a robust statistic-based algorithm, and introduces methods for differentially private confidence intervals.

Findings

Provides finite-sample privacy and accuracy bounds

Guides hyperparameter selection for DPTheilSen

Demonstrates how to construct differentially private confidence intervals

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.