Functional Mechanism: Regression Analysis under Differential Privacy

TL;DR

The paper introduces the Functional Mechanism, a novel approach for achieving epsilon-differential privacy in regression analysis by perturbing the objective function, leading to more accurate and efficient results for linear and logistic regression.

Contribution

It presents the first general method for differentially private regression analysis that applies to a broad class of optimization problems by perturbing the objective function.

Findings

Outperforms existing privacy-preserving regression methods in accuracy.

Efficiently applies to both linear and logistic regression models.

Theoretically guarantees epsilon-differential privacy.

Abstract

\epsilon-differential privacy is the state-of-the-art model for releasing sensitive information while protecting privacy. Numerous methods have been proposed to enforce epsilon-differential privacy in various analytical tasks, e.g., regression analysis. Existing solutions for regression analysis, however, are either limited to non-standard types of regression or unable to produce accurate regression results. Motivated by this, we propose the Functional Mechanism, a differentially private method designed for a large class of optimization-based analyses. The main idea is to enforce epsilon-differential privacy by perturbing the objective function of the optimization problem, rather than its results. As case studies, we apply the functional mechanism to address two most widely used regression models, namely, linear regression and logistic regression. Both theoretical analysis and thorough experimental evaluations show that the functional mechanism is highly effective and efficient, and it significantly outperforms existing solutions.