Bo Jiang

Bo Jiang, Ming Li, Ravi Tandon

In this paper, we study local information privacy (LIP), and design LIP based mechanisms for statistical aggregation while protecting users' privacy without relying on a trusted third party. The notion of context-awareness is incorporated in LIP, which can be viewed as explicit modeling of the adversary's background knowledge. It enables the design of privacy-preserving mechanisms leveraging the prior distribution, which can potentially achieve a better utility-privacy tradeoff than context-free notions such as Local Differential Privacy (LDP). We present an optimization framework to minimize the mean square error in the data aggregation while protecting the privacy of each individual user's input data or a correlated latent variable while satisfying LIP constraints. Then, we study two different types of applications: (weighted) summation and histogram estimation and derive the optimal context-aware data perturbation parameters for each case, based on randomized response type of mechanism. We further compare the utility-privacy tradeoff between LIP and LDP and theoretically explain why the incorporation of prior knowledge enlarges feasible regions of the perturbation parameters, which thereby leads to higher utility. We also extend the LIP-based privacy mechanisms to the more general case when exact prior knowledge is not available. Finally, we validate our analysis by simulations using both synthetic and real-world data. Results show that our LIP-based privacy mechanism provides better utility-privacy tradeoffs than LDP, and the advantage of LIP is even more significant when the prior distribution is more skewed.

Bo Jiang, Ming Li, Ravi Tandon

In this paper, localized information privacy (LIP) is proposed, as a new privacy definition, which allows statistical aggregation while protecting users' privacy without relying on a trusted third party. The notion of context-awareness is incorporated in LIP by the introduction of priors, which enables the design of privacy-preserving data aggregation with knowledge of priors. We show that LIP relaxes the Localized Differential Privacy (LDP) notion by explicitly modeling the adversary's knowledge. However, it is stricter than $2ε$-LDP and $ε$-mutual information privacy. The incorporation of local priors allows LIP to achieve higher utility compared to other approaches. We then present an optimization framework for privacy-preserving data aggregation, with the goal of minimizing the expected squared error while satisfying the LIP privacy constraints. Utility-privacy tradeoffs are obtained under several models in closed-form. We then validate our analysis by {numerical analysis} using both synthetic and real-world data. Results show that our LIP mechanism provides better utility-privacy tradeoffs than LDP and when the prior is not uniformly distributed, the advantage of LIP is even more significant.