Learning from users’ data has demonstrated to be tremendously effective at solving many real-world problems. However, such paradigm comes with new challenges such as users’ privacy. Differential Privacy was proposed as a way to bound the information quantity leaked by statistics in order to bound the power of membership tests, hence giving strong guarantees for users’ privacy. Being a rather strong constraint, it comes at a cost on the quality of estimation. A natural question is thus to quantify this cost, and to compare it to the already-existing sampling noise. In this presentation, we will see a generic way to quantify this cost via coupling arguments, and we will illustrate it by examples ranging from simple Bernoulli estimation to nonparametric density estimation.
