Learning the intensity of time events with change-points

Abstract : We consider the problem of learning the inhomogeneous intensity of a counting process, under a sparse segmentation assumption. We introduce a weighted total-variation penalization, using data-driven weights that correctly scale the penalization along the observation interval. We prove that this leads to a sharp tuning of the convex relaxation of the segmentation prior, by stating oracle inequalities with fast rates of convergence, and consistency for change-points detection. This provides first theoretical guarantees for segmentation with a convex proxy beyond the standard i.i.d signal + white noise setting. We introduce a fast algorithm to solve this convex problem. Numerical experiments illustrate our approach on simulated and on a high-frequency genomics dataset.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01163415
Contributeur : Mokhtar Z. Alaya <>
Soumis le : vendredi 12 juin 2015 - 18:09:22
Dernière modification le : mercredi 28 novembre 2018 - 01:23:15
Document(s) archivé(s) le : mardi 25 avril 2017 - 07:43:27

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  • HAL Id : hal-01163415, version 1
  • ARXIV : 1507.00513

Citation

Mokhtar Z. Alaya, Stéphane Gaïffas, Agathe Guilloux. Learning the intensity of time events with change-points. 2015. 〈hal-01163415〉

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