Probabilizing the segmentation space in local score approaches

We are interested here in 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 the local score approach 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/end-ing indexes. We explain how this equivalence allows to manage ambiguous or uncertain sequence letters and to construct relevant scoring schemes. We illustrate our approach by considering the TM-tendency scoring function