  \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.
