Exploring the segmentation space for the assessment of multiple change-point models

Yann Guédon (1, 2)

1 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
2 UMR DAP - Développement et amélioration des plantes

This paper addresses the retrospective or off-line multiple change-point detection problem. Methods for exploring the space of possible segmentations of a sequence for a fixed number of change points may be divided into two categories: (i) enumeration of segmentations, (ii) summary of the possible segmentations in change-point or segment profiles. Concerning the first category, a forward dynamic programming algorithm for computing the top L most probable segmentations and a forward-backward algorithm for sampling segmentations are derived. Concerning the second category, a forward-backward dynamic programming algorithm and a smoothing-type forward-backward algorithm for computing two types of change-point and segment profiles are derived. The proposed methods are mainly useful for exploring the space of possible segmentations for successive numbers of change points and provide a set of assessment tools for multiple change-point models. We show using examples that the proposed methods may help to compare alternative multiple change-point models (e.g. Gaussian model with piecewise constant variances or global variance), predict supplementary change points, highlight overestimation of the number of change points and summarize the uncertainty concerning the location of change points.

Mots clés: dynamic programming algorithm; multiple change-point detection; plant structure analysis; smoothing algorithm

Domaines: Statistiques [math.ST]

Yann Guédon. Exploring the segmentation space for the assessment of multiple change-point models. [Research Report] RR-6619, INRIA. 2008, pp.37. ⟨inria-00311634⟩