Differential privacy is the state-of-the-art formal definition for data release under strong privacy guarantees. A variety of mechanisms have been proposed in the literature for releasing the noisy output of numeric queries (e.g., using the Laplace mechanism), based on the notions of global sensitivity and local sensitivity. However, although there has been some work on generic mechanisms for releasing the output of non-numeric queries using global sensitivity (e.g., the Exponential mechanism), the literature lacks generic mechanisms for releasing the output of non-numeric queries using local sensitivity to reduce the noise in the query output. In this work, we remedy this shortcoming and present the local dampening mechanism. We adapt the notion of local sensitivity for the non-numeric setting and leverage it to design a generic non-numeric mechanism. We illustrate the effectiveness of the local dampening mechanism by applying it to two diverse problems: (i) Influential node analysis. Given an influence metric, we release the top-k most central nodes while preserving the privacy of the relationship between nodes in the network; (ii) Decision tree induction. We provide a private adaptation to the ID3 algorithm to build decision trees from a given tabular dataset. Experimental results show that we could reduce the use of privacy budget by 3 to 4 orders of magnitude for Influential node analysis and increase accuracy up to 12% for Decision tree induction when compared to global sensitivity based approaches.
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