  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 $2\epsilon$-LDP and $\epsilon$-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.
