Functional mechanism

TLDR

ε‑differential privacy is the leading framework for releasing sensitive data, yet existing regression‑based methods are either restricted to non‑standard models or yield inaccurate results. This work introduces the Functional Mechanism, a differentially private approach applicable to a broad class of optimization‑based analyses. The method achieves privacy by perturbing the objective function of the optimization problem, and is demonstrated on linear and logistic regression. Theoretical proofs and extensive experiments show that the Functional Mechanism outperforms prior solutions in both accuracy and efficiency.

Abstract

ε-differential privacy is the state-of-the-art model for releasing sensitive information while protecting privacy. Numerous methods have been proposed to enforce ε-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 ε-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.