Individual Sensitivity Preprocessing for Data Privacy
Rachel Cummings, David Durfee · Society for Industrial and Applied Mathematics eBooks · 2019
The sensitivity metric in differential privacy, which is informally defined as the largest marginal change in output between neighboring databases, is of substantial significance in determining the accuracy of private data analyses. Techniques for improving accuracy when the average sensitivity is much smaller than the worst-case sensitivity have been developed within the differential privacy literature, including tools such as smooth sensitivity, Sample-and-Aggregate, Propose-Test-Release, and Lipschitz extensions. In this work, we provide a new and general Sensitivity-Preprocessing framework for reducing sensitivity, where efficient application gives state-of-the-art accuracy for privately outputting the important statistical metrics median and mean when no underlying assumptions are made about the database. In particular, our framework compares favorably to smooth sensitivity for privately outputting median, in terms of both running time and accuracy. Furthermore, because our framework is a preprocessing step, it can also be complementary to smooth sensitivity and any other private mechanism, where applying both can achieve further gains in accuracy. We additionally introduce a new notion of individual sensitivity and show that it is an important metric in the variant definition of personalized differential privacy. We show that our algorithm can extend to this context and serve as a useful tool for this variant definition and its applications in markets for privacy. Given the effectiveness of our framework in these important statistical metrics, we further investigate its properties and show that: (1) Our construction is conducive to efficient implementation with strong accuracy guarantees, evidenced by an O(n) implementation for median (with presorted data), and O(n2) implementation for more complicated functions such as mean, α-trimmed mean, and variance. (2) Our construction is both NP-hard and also optimal in the general setting (3) Our construction can be extended to higher dimensions, although it incurs accuracy loss that is linear in the dimension.