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Local Information Privacy with Bounded Prior

A localized privacy protection notion: local information privacy (LIP) is studied in this paper. As a context-aware notion that considers prior knowledge, the LIP notion is shown to provide increased utility than local differential privacy (LDP). Within the scope of LIP, we further consider scenarios with uncertainty on the prior knowledge, i.e., the prior is bounded within a certain range or the prior is arbitrary. The former case is defined as bounded-prior LIP (BP-LIP), and the latter as worst-case LIP (WC-LIP). The contributions of this paper are three-fold: We first provide theoretical results which show the connections of these new definitions with LDP; Secondly, we present an optimization framework for privacy-preserving data collection, with the goal of minimizing the expected squared error while satisfying BP-LIP and WC-LIP privacy constraints. Utility-privacy tradeoffs are obtained in closed-form. At last, we validate our conclusions by numerical analysis and real-world data simulation. Our results show that the notion of bounded-prior LIP can achieve better utility-privacy tradeoff compared to context free notion of LDP.