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

• Published in: Computational statistics Vol. 28; no. 6; pp. 2641 - 2678
• Main Author: Guedon, Yann
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2013; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Analysis; By products; Computer Science; Data smoothing; Dynamic programming; Economic Theory/Quantitative Economics/Mathematical Methods; Markov analysis; Mathematics and Statistics; Modeling and Simulation; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Studies; Dynamic programming algorithm; Latent structure model; Multiple change-point detection; Plant structure analysis; Smoothing algorithm; detection; latent; plant; multiple; dynamic; model; smoothing; analysis; change-point; programming; structure; algorithm
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-013-0422-9

This paper addresses the retrospective or off-line multiple change-point detection problem. Multiple change-point models are here viewed as latent structure models and the focus is on inference concerning the latent segmentation space. 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 dynamic programming algorithm for computing the top N most probable segmentations is 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 segmentation space for successive numbers of change points and provide a set of assessment tools for multiple change-point models that can be applied both in a non-Bayesian and a Bayesian framework. 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 position of change points.