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Differential privacy provides strong privacy guarantees simultaneouslyenabling useful insights from sensitive datasets. However, it provides the samelevel of protection for all elements (individuals and attributes) in the data.There are practical scenarios where some data attributes need more/lessprotection than others. In this paper, we consider $d_{\mathcal{X}}$-privacy,an instantiation of the privacy notion introduced in\cite{chatzikokolakis2013broadening}, which allows this flexibility byspecifying a separate privacy budget for each pair of elements in the datadomain. We describe a systematic procedure to tailor any existingdifferentially private mechanism that assumes a query set and a sensitivityvector as input into its $d_{\mathcal{X}}$-private variant, specificallyfocusing on linear queries. Our proposed meta procedure has broad applicationsas linear queries form the basis of a range of data analysis and machinelearning algorithms, and the ability to define a more flexible privacy budgetacross the data domain results in improved privacy/utility tradeoff in theseapplications. We propose several $d_{\mathcal{X}}$-private mechanisms, andprovide theoretical guarantees on the trade-off between utility and privacy. Wealso experimentally demonstrate the effectiveness of our procedure, byevaluating our proposed $d_{\mathcal{X}}$-private Laplace mechanism on bothsynthetic and real datasets using a set of randomly generated linear queries.

Not All Attributes are Created Equal: $d_{\mathcal{X}}$-Private Mechanisms for Linear Queries