Duality between the local score of one sequence and constrained Hidden Markov Model

Sabine Mercier (1) , Gregory Nuel (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Mots clés: biological sequence analysis; forward/backward; Local score; maximum scoring subsequence; HMM; posterior distribution

Domaines: Probabilités [math.PR]

Sabine Mercier, Gregory Nuel. Duality between the local score of one sequence and constrained Hidden Markov Model. Methodology and Computing in Applied Probability, 2021, Methodology and Computing in Applied Probability, 24, pp.1411-1438. ⟨hal-02179477v2⟩