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

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 c...

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Vydané v:	Methodology and computing in applied probability Ročník 24; číslo 3; s. 1411 - 1438
Hlavní autori:	Mercier, Sabine, Nuel, Grégory
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.09.2022 Springer Nature B.V Springer Verlag
Edícia:	Methodology and Computing in Applied Probability
Predmet:	Adaptation Algorithms Business and Management Economics Electrical Engineering Equivalence Life Sciences Markov chains Mathematics Mathematics and Statistics Probability Segmentation Segments Statistics Maximum scoring subsequence 60J20 62M05 62C10 Local score HMM Forward/backward 60 Posterior distribution Biological sequence analysis 62F15 forward/backward maximum scoring subsequence posterior distribution biological sequence analysis
ISSN:	1387-5841, 1573-7713
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Popis
Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1387-5841 1573-7713
DOI:	10.1007/s11009-021-09856-8