Optimal multiple change-point detection for high-dimensional data
Résumé
This manuscript makes two contributions to the field of change-point detection. In a general
change-point setting, we provide a generic algorithm for aggregating local homogeneity tests
into an estimator of change-points in a time series. Interestingly, we establish that the error
rates of the collection of tests directly translate into detection properties of the change-point
estimator. This generic scheme is then applied to various problems including covariance change-
point detection, nonparametric change-point detection and sparse multivariate mean change-
point detection. For the latter, we derive minimax optimal rates that are adaptive to the
unknown sparsity and to the distance between change-points when the noise is Gaussian. For
sub-Gaussian noise, we introduce a variant that is optimal in almost all sparsity regimes.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)