Optimal multiple change-point detection for high-dimensional data

This manuscript makes two contributions to the field of change-point detection. In a general setting, we provide generic algorithm for aggregating local homogeneity tests into an estimator change-points in time series. Interestingly, establish that error rates collection directly translate detection properties estimator. scheme is then applied various problems including covariance detection, nonparametric and sparse multivariate mean For latter, derive minimax optimal are adaptive unknown sparsity distance between when noise Gaussian. sub-Gaussian noise, introduce variant almost all regimes.