Learning the intensity of time events with change-points

Mokhtar Zahdi Alaya; Stéphane Gaïffas; Agathe Guilloux

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arXiv · 1507.00513

Learning the intensity of time events with change-points

Mokhtar Zahdi Alaya·Stéphane Gaïffas·Agathe Guilloux

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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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BibTeX RIS

Mokhtar Zahdi Alaya, Stéphane Gaïffas, Agathe Guilloux. 2015-07-02. Learning the intensity of time events with change-points. https://arxiv.org/abs/1507.00513

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