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October 15, 2025Open Access

Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models

AMAlexandre MöschingRoche (Switzerland)HLHousen LiTH Bingen University of Applied Sciences AMAxel MunkUniversity of Göttingen

Key Points

The proposed decoding method offers significant improvements in efficiency over conventional algorithms.
Existing algorithms like Viterbi and PMAP face challenges in terms of computational complexity.
The new approach maintains linear complexity with respect to observation length and enhances adaptability to state space size.
Developing efficient decoding procedures can greatly impact data analysis tasks utilizing hidden markov models.

Abstract

Hidden Markov models (HMMs) are characterized by an unobservable Markov chain and an observable process—a noisy version of the hidden chain. Decoding the original signal from the noisy observations is one of the main goals in nearly all HMM based data analyses. Existing decoding algorithms such as Viterbi and the pointwise maximum a posteriori (PMAP) algorithm have computational complexity at best linear in the length of the observed sequence, and sub-quadratic in the size of the state space of the hidden chain.

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