Truthful Linear Regression

TL;DR

This paper addresses the challenge of fitting linear models to privacy-sensitive data by designing mechanisms that ensure truthful reporting while respecting differential privacy, overcoming bias issues inherent in private computations.

Contribution

It introduces a novel mechanism design that enables truthful data reporting and accurate linear regression under differential privacy constraints.

Findings

Mechanism achieves truthful reporting of sensitive data.

Ensures differential privacy in linear regression.

Addresses bias issues in private estimations.

Abstract

We consider the problem of fitting a linear model to data held by individuals who are concerned about their privacy. Incentivizing most players to truthfully report their data to the analyst constrains our design to mechanisms that provide a privacy guarantee to the participants; we use differential privacy to model individuals' privacy losses. This immediately poses a problem, as differentially private computation of a linear model necessarily produces a biased estimation, and existing approaches to design mechanisms to elicit data from privacy-sensitive individuals do not generalize well to biased estimators. We overcome this challenge through an appropriate design of the computation and payment scheme.