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Segmentation uncertainty in multiple change-point models

机译：多变更点模型中的分割不确定性

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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.
机译：本文解决了追溯或离线多变化点检测问题。在这种情况下，需要有效的诊断工具，其能够沿着观察到的序列定位分割不确定性。关于分割的不确定性，重点主要在于变化点位置的不确定性。我们建议以一种新的方式陈述这个问题，将多个变更点模型视为潜在结构模型并使用信息论的结果。这导致我们表明，由于不确定性在这些后验分布的计算中是固有的，因此分割不确定性未反映在变化点位置的后验分布中。给定观测序列的分割熵可以视为分割不确定性的标准度量。可以将这种分割熵分解为条件熵概图，从而可以沿着序列定位该规范的分割不确定性。这项工作的主要成果之一是获得有效的算法来计算这些条件熵分布图。拟议的方法得益于Shannon-Khinchin熵公理的所有属性，因此是沿序列定位规范分割不确定性的独特方法。我们引入了连续分布的变化点数目的分割分布的均匀分布的Kullback-Leibler散度，作为评估通过不同方法选择的变化点数目的新工具。使用四个对比示例说明了所提出的方法。

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