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Differentially Private Linear Regression With Linked Data

Forthcoming. Now Available: Just Accepted Version.
Published onJul 09, 2024
Differentially Private Linear Regression With Linked Data


There has been increasing demand for establishing privacy-preserving methodologies for modern statistics and machine learning. Differential privacy, a mathematical notion from computer science, is a rising tool offering robust privacy guarantees. Recent work focuses primarily on developing differentially private versions o f individual statistical and machine learning tasks, with nontrivial upstream pre-processing typically not incorporated. An important example is when record linkage is done prior to downstream modeling. Record linkage refers to the statistical task of linking two or more datasets of the same group of entities without a unique identifier. This probabilistic procedure brings additional uncertainty to the subsequent task. In this paper, we present two differentially private algorithms for linear regression with linked data. In particular, we propose a noisy gradient method and a sufficient statistics perturbation approach for the estimation of regression coefficients. We investigate the privacy-accuracy tradeoff by providing finite-sample error bounds for the estimators, which allows us to understand the relative contributions of linkage error, estimation error, and the cost of privacy. The variances of the estimators are also discussed. We demonstrate the performance of the proposed algorithms through simulations and an application to synthetic data.

Keywords: differential privacy, record linkage, data integration, privacy-preserving record linkage, gradient descent

07/09/2024: To preview this content, click below for the Just Accepted version of the article. This peer-reviewed version has been accepted for its content and is currently being copyedited to conform with HDSR’s style and formatting requirements.

©2024 Shurong Lin, Elliot Paquette, and Eric D. Kolaczyk. This article is licensed under a Creative Commons Attribution (CC BY 4.0) International license, except where otherwise indicated with respect to particular material included in the article.

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