Cost-based recommendation of parameters for local differentially private data aggregation

Abstract

The ability to analyze personal data for a group of individuals without compromising their respective privacy has been a focus of significant research in recent years. For such analyses, data analysts need to acquire data from individuals without revealing their Individually Identifiable Data (IID). Well established Differentially Private techniques, characterized by privacy parameters (ϵ,δ), transform the data to protect the IID. However, such transformations adversely affect the usefulness of data leading to a trade-off between usefulness and privacy. Therefore, negotiating appropriate values of privacy parameters before data acquisition is a challenging task for data analysts. Most of the work, in selecting values of privacy parameters, is either based on constraining all other parameters or they provide a set of acceptable values. Here also the problem of selecting the best value from the set of acceptable values is left to the analyst. A major contribution of this paper is the method of identifying the best value of privacy parameters in a trade-off between usefulness and privacy by introducing a cost-based model, thereby addressing the issue. To enable estimation of usefulness and its cost before data acquisition, we have mathematically modeled utility in terms of data and privacy parameters. We have considered standard statistical aggregates such as Sum, Mean and Standard Deviation as compared to most of the existing works that consider only Count query as aggregate analysis. The correctness of our mathematical estimation has been validated on a diverse set of synthetic and real-world datasets spanning popular data distributions.