Duality Between the Local Score of One Sequence and Constrained Hidden Markov Model

Sabine Mercier () and Grégory Nuel ()
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Sabine Mercier: Université de Toulouse 2 Jean Jaurès
Grégory Nuel: Laboratoire de Probabilités Statistique Modélisation (LPSM), CNRS 8001Sorbonne Université

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1411-1438

Abstract: Abstract 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.

Keywords: Local score; Maximum scoring subsequence; HMM; Posterior distribution; Forward/backward; Biological sequence analysis; 60; 60J20; 62M05; 62F15; 62C10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09856-8

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