Title: Estimating linear and quadratic functionals under local differential privacy
Authors: Lukas Steinberger - University of Vienna (Austria) [presenting]
Abstract: In the local paradigm of differential privacy, we study the problem of estimating a functional of the true unknown data generating distribution. For linear functionals over convex parameter spaces, we develop a general minimax theory of private estimation. We find that appropriately privatized sample mean type estimators are always minimax optimal and, in particular, that local privacy protocols that allow for some sequential interaction between data providers do not improve significantly over purely non-interactive protocols. These facts are no longer true for non-linear functionals. For estimation of the integrated square of the density over Besov spaces, we present a locally private estimator that is sequential in nature and improves over the best non-interactive procedure in terms of minimax rate.