Optimal multiple change-point detection for high-dimensional data

Emmanuel Pilliat (1) , Alexandra Carpentier (2) , Nicolas Verzelen (3)

1 UM - Université de Montpellier
2 Institut für Mathematik [Potsdam]
3 INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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: Statistiques [math.ST]

Emmanuel Pilliat, Alexandra Carpentier, Nicolas Verzelen. Optimal multiple change-point detection for high-dimensional data. 2022. ⟨hal-03004860v3⟩