Learning the intensity of time events with change-points
This work addresses the challenge of accurately segmenting time event intensities, which is incremental as it extends convex relaxation methods beyond standard i.i.d. settings to provide theoretical guarantees for change-point detection.
The paper tackles the problem of learning the inhomogeneous intensity of a counting process under sparse segmentation assumptions by introducing a weighted total-variation penalization with data-driven weights, achieving fast convergence rates and consistency in change-point detection. Numerical experiments demonstrate its effectiveness on simulated and high-frequency genomics data.
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.