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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.
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https://hal.archives-ouvertes.fr/hal-01163415
Contributor : Mokhtar Z. Alaya <>
Submitted on : Friday, June 12, 2015 - 6:09:22 PM
Last modification on : Thursday, March 5, 2020 - 6:30:33 PM
Document(s) archivé(s) le : Tuesday, April 25, 2017 - 7:43:27 AM

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Identifiers

  • 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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