Differentially Private Simple Linear Regression

Abstract Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets the data. Unfortunately, such fine-grained analysis can easily reveal individual information. We study regression algorithms that satisfy differential privacy , a constraint which guarantees an algorithm’s output reveals little about any input data record, even attacker side dataset. Motivated by Opportunity Atlas high-profile, small-area tool in economics research, we perform thorough experimental evaluation differentially private for simple linear on tens hundreds records—a particularly challenging regime privacy. In contrast, prior work focused multivariate large or asymptotic analysis. Through range experiments, identify key factors affect relative performance algorithms. find based robust estimators—in particular, median-based estimator Theil Sen—perform best (e.g., datapoints), while Ordinary Least Squares Gradient Descent better datasets. However, also discuss regimes this general finding does not hold. Notably, analogues Theil–Sen (one was suggested theoretical Dwork Lei) have been studied regression.