Differential Privacy in distribution and instance-based noise mechanisms

In this paper, we introduce the notion of ( , δ)-differential privacy in distribution, a strong version of the existing ( , δ)-differential privacy, used to mathematically ensure that private data of an individual are protected when embedded into a queried database. In practice, such property is obtained by adding some relevant noise. Our new notion permits to simplify proofs of ( , δ) privacy for mechanisms adding noise with a continuous distribution. As a first example, we give a simple proof that the Gaussian mechanism is ( , δ)-differentially private in distribution. Using differential privacy in distribution, we then give simple conditions for an instance-based noise mechanism to be ( , δ)-differentially private. After that, we exploit these conditions to design a new ( , δ)-differentially private instance-based noise algorithm. Compare to existing ones, our algorithm have a better accuracy when used to answer a query in a differentially private manner. In particular, our algorithm does not require the computation of the so-called Smooth Sensitivity, usually used in instance-based noise algorithms, and which was proved to be NP hard to compute in some cases, namely statistics queries on some graphs. Our algorithm handles such situations and in particular some cases for which no instance-based noise mechanism were known to perform well.