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.
- J. Zhang, Z. Zhang, X. Xiao, Y. Yang and M. Winslett. Functional Mechanism: Regresssion Analysis under Differential Privacy, VLDB, 2012.