We are interested here in a theoretical and practical approach for detecting atypical segments in a multi-state sequence. We prove in this article that the segmentation approach through an underlying constrained Hidden Markov Model (HMM) is equivalent to using the maximum scoring subsequence (also called local score), when the latter uses an appropriate rescaled scoring function. This equivalence allows results from both HMM or local score to be transposed into each other. We propose an adaptation of the standard forward-backward algorithm which provides exact estimates of posterior probabilities in a linear time. Additionally it can provide posterior probabilities on the segment length and starting/ending indexes. We explain how this equivalence allows one to manage ambiguous or uncertain sequence letters and to construct relevant scoring functions. We illustrate our approach by considering the TM-tendency scoring function.

我们在这里对在多状态序列中检测非典型片段的理论和实践方法感兴趣。我们在本文中证明，通过基础约束隐式马尔可夫模型（HMM）进行的分割方法等效于使用最大评分子序列（也称为局部评分），而后者使用了适当的重新缩放评分功能。这种等效性允许来自HMM或本地得分的结果相互转换。我们提出了一种标准的向前-向后算法的改编，该算法提供了线性时间中后验概率的精确估计。另外，它可以提供段长度和起始/结束索引的后验概率。我们解释了这种等效性如何使人们能够处理歧义或不确定的序列字母并构建相关的评分功能。我们通过考虑TM倾向评分功能来说明我们的方法。