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    Area of Science:

    • Computational Biology
    • Statistical Modeling
    • Machine Learning

    Background:

    • Hidden Markov Models (HMMs) are effective for sequential data but traditional models are limited to linear structures.
    • Existing extensions of HMMs to tree structures do not fully capture dependencies within coupled branches, common in biological systems.

    Purpose of the Study:

    • To extend the framework of HMMs on trees to incorporate coupled branches, addressing data with lineage-dependent characteristics.
    • To develop an efficient dynamic programming algorithm for likelihood, decoding, and parameter learning in these complex HMMs.

    Main Methods:

    • Development of a novel dynamic programming algorithm tailored for tree-based HMMs with coupled branches.
    • The algorithm efficiently computes likelihood, performs decoding, and learns parameters.
    • Polynomial scaling with the number of states and nodes ensures computational feasibility and avoids the underflow problem.

    Main Results:

    • The proposed algorithm successfully handles HMMs on trees with coupled branches.
    • Demonstrated application on simulated data confirms the algorithm's efficacy.
    • The method provides a practical tool for analyzing complex biological data with inherent branching dependencies.

    Conclusions:

    • This work advances the theoretical understanding of HMMs on tree structures.
    • The developed algorithm offers a computationally efficient and robust solution for modeling biological data with coupled branches.
    • Introduces self-consistency checks for model validation in inference.