  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.
