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results consider the more general case with multiple privacy level relaxations and show that there exists a composite mechanism that achieves no loss
We consider the case in which the private data lies within Rn with an adjacency relation induced by the \( \ell _1\)-norm, and we initially focus on mechanisms that approximate identity queries. We show that the same accuracy can be achieved in the case of gradual release through a mechanism whose outputs can be described by a lazy Markov stochastic process. This stochastic process has a closed form expression and can be efficiently sampled. Moreover, our results extend beyond identity queries to a more general family of privacy-preserving mechanisms. To this end, we demonstrate the applicability of our tool to multiple scenarios including Google’s project RAPPOR, trading of private data, and controlled transmission of private data in a social network. Finally, we derive similar results for the approximated differential privacy.
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