The Bernstein Mechanism: Function Release under Differential Privacy

Abstract

We address the problem of general function release under differential privacy, by developing a functional mechanism that applies under the weak assumptions of oracle access to target function evaluation and sensitivity. These conditions permit treatment of functions described explicitly or implicitly as algorithmic black boxes. We achieve this result by leveraging the iterated Bernstein operator for polynomial approximation of the target function, and polynomial coefficient perturbation. Under weak regularity conditions, we establish fast rates on utility measured by high-probability uniform approximation. We provide a lower bound on the utility achievable for any functional mechanism that is epsilon-differentially private. The generality of our mechanism is demonstrated by the analysis of a number of example learners, including naive Bayes, non-parametric estimators and regularized empirical risk minimization. Competitive rates are demonstrated for kernel density estimation; and epsilon-differential privacy is achieved for a broader class of support vector machines than known previously.

A Study on Quantized Parameters for Protection of a Model and Its Inference Input

“…Protection of a model can also be provided by differential privacy [47]. There is a study on the protection of a model via differential privacy [48]. However, differential privacy is ineffective in the inference phase, and hence secure computation is necessary [15].…”