Locally private online change point detection

We study online change point detection problems under the constraint of local differential privacy (LDP) where, in particular, the statistician does not have access to the raw data. As a concrete problem, we study a multivariate nonparametric regression problem. At each time point t, the raw data are assumed to be of the form (X_t, Y_t), where X_t is a d -dimensional feature vector and Y_t is a response variable. Our primary aim is to detect changes in the regression function m_t(x) \mathbb{E}(Y_t X_t x) as soon as the change occurs. We provide algorithms which respect the LDP constraint, which control the false alarm probability, and which detect changes with a minimal (minimax rate-optimal) delay.