  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. To quantify the cost of privacy, we also
present the optimal rate in the benchmark, non-private setting. These
non-private results are also new to the literature and thus are interesting
\emph{per se}. In addition, we study the univariate mean online change point
detection problem, under privacy constraints. This serves as the blueprint of
studying more complicated private change point detection problems.
