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Journal Articles Electronic Journal of Statistics Year : 2023

Optimal multiple change-point detection for high-dimensional data

Abstract

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.
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hal-04305116 , version 1 (24-11-2023)

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Emmanuel Pilliat, Alexandra Carpentier, Nicolas Verzelen. Optimal multiple change-point detection for high-dimensional data. Electronic Journal of Statistics , 2023, 17 (1), pp.1240-1315. ⟨10.1214/23-ejs2126⟩. ⟨hal-04305116⟩
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