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.

翻译：本地差异隐私(LDP)的制约下,我们研究在线变化点检测问题,特别是统计员无法获取原始数据。作为一个具体问题,我们研究的是多变量的非参数回归问题。在每次点美元时,我们假定原始数据为美元(X_t,Y_t),美元是美元(美元)的维基质矢量,而美元(Y_t)是一个响应变量。我们的主要目的,是发现回归函数($m_t)(x) ⁇ mathb{E}(Y_t ⁇ X_t=x)的变化。我们提供算法,以尊重LDP的制约,控制错误警报概率,并在最小(最小速率-最佳)延迟的情况下检测变化。为了量化隐私成本,我们还在基准和非私人设置中展示了最佳的速率。这些非私人结果对文献来说也是新的,因此很有意思的\emph{se}。此外,我们提供一种尊重LDP限制的算法,以最小(最小速率-最优化的)时间来检测隐私问题。