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Pré-Publication, Document De Travail Année : 2020

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 test directly translate into detection properties of the change-point estimator. This generic scheme is then applied to the problem of possibly sparse multivariate mean change-point detection setting. When the noise is Gaussian, we derive minimax optimal rates that are adaptive to the unknown sparsity and to the distance between change-points. For sub-Gaussian noise, we introduce a variant that is optimal in almost all sparsity regimes.
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Dates et versions

hal-03004860 , version 1 (13-11-2020)
hal-03004860 , version 2 (21-07-2021)
hal-03004860 , version 3 (07-12-2022)

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Emmanuel Pilliat, Alexandra Carpentier, Nicolas Verzelen. Optimal multiple change-point detection for high-dimensional data. 2020. ⟨hal-03004860v1⟩
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