Séance Séminaire

Séminaire de Probabilités et Statistique

Segmentation uncertainty in multiple change-point models

We address the retrospective or off-line multiple change-point detection problem. Concerning the segmentation uncertainty in multiple change-point models, the focus was mainly on the change-point position uncertainty. We propose to state this problem in a new way, viewing multiple change-point models as latent structure models and using results from information theory. This led us to show that the posterior distributions of the change-point position only reflect partially the segmentation uncertainty. The canonical uncertainty is given by the posterior distribution of the segmentations. The corresponding segmentation entropy can be decomposed as an entropy profile which enables to localize this canonical uncertainty along the sequence. We propose to use the Kullback-Leibler divergence of the uniform distribution from the segmentation distribution for successive numbers of change points as a new adaptive criterion for selecting the number of change points. An in-depth introspection of the segmentation posterior distributions for successive numbers of change points using different examples demonstrates the accuracy of the proposed criterion.

Keywords. Entropy; Kullback-Leibler divergence; Latent structure model; Multiple change-point detection; Smoothing algorithm.