NDLI: Segmentation uncertainty in multiple change-point models

Content Provider	Springer Nature Link
Author	Guédon, Yann
Copyright Year	2013
Abstract	This paper addresses the retrospective or off-line multiple change-point detection problem. In this context, there is a need of efficient diagnostic tools that enable to localize the segmentation uncertainty along the observed sequence. Concerning the segmentation uncertainty, 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 segmentation uncertainty is not reflected in the posterior distributions of the change-point position because of the marginalization that is intrinsic in the computation of these posterior distributions. The entropy of the segmentation of a given observed sequence can be considered as the canonical measure of segmentation uncertainty. This segmentation entropy can be decomposed as conditional entropy profiles that enables to localize this canonical segmentation uncertainty along the sequence. One of the main outcomes of this work is to derive efficient algorithms to compute these conditional entropy profiles. The proposed approach benefits from all the properties of the Shannon–Khinchin axioms of entropy and therefore is the unique approach for localizing the canonical segmentation uncertainty along the sequence. We introduce the Kullback–Leibler divergence of the uniform distribution from the segmentation distribution for successive numbers of change points as a new tool for assessing the number of change points selected by different methods. The proposed approach is illustrated using four contrasted examples.
Starting Page	303
Ending Page	320
Page Count	18
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	25
Issue Number	2
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2013-12-06
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Entropy Kullback–Leibler divergence Latent structure model Multiple change-point detection Smoothing algorithm Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistical Theory and Methods Probability and Statistics in Computer Science
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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