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Article Dans Une Revue IEEE Transactions on Information Theory Année : 2015

Learning the intensity of time events with change-points

Résumé

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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Dates et versions

hal-01163415 , version 1 (12-06-2015)

Identifiants

Citer

Mokhtar Z. Alaya, Stéphane Gaïffas, Agathe Guilloux. Learning the intensity of time events with change-points. IEEE Transactions on Information Theory, 2015, 61 (9), pp.5148-5171. ⟨hal-01163415⟩
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