Differentially Private Nonlinear Observers

This chapter introduces tools for the design of differentially private nonlinear dynamic observers. Indeed, the dynamic models useful to estimate and predict the characteristics of a population, originating for example from epidemiology or the social sciences, are often nonlinear. The main issue discussed is the computation of the sensitivity of a class of nonlinear observers, which is necessary to design differentially private output perturbation or two-stage mechanisms, when the first stage is nonlinear. We use here contraction analysis in order to design convergent observers with appropriately controlled sensitivity. Two examples are also discussed for illustration purposes: estimating the edge formation probabilities in a social network using a dynamic stochastic block model, and syndromic surveillance relying on an epidemiological model.