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  1. Home
  3. An Efficient Solution To Hidden Markov Models On Trees With Coupled Branches.
  1. Home
  3. An Efficient Solution To Hidden Markov Models On Trees With Coupled Branches.

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Automatic Identification of Dendritic Branches and their Orientation
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An efficient solution to Hidden Markov Models on trees with coupled branches.

Farzan Vafa1, Sahand Hormoz2

  • 1Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA. He is now with the Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA, and also with the Department of Data Science, Dana-Farber Cancer Institute, Boston, MA 02215 USA.

IEEE Transactions on Signal Processing : a Publication of the IEEE Signal Processing Society
|December 4, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

We introduce a new dynamic programming algorithm for Hidden Markov Models (HMMs) on trees with coupled branches, enhancing biological data analysis. This method efficiently handles complex dependencies without underflow issues.

Keywords:
Dynamic ProgrammingExpectation MaximizationHierarchical DataStatistical InferenceUnderflow Problem

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Area of Science:

  • Computational Biology
  • Statistical Modeling
  • Machine Learning

Background:

  • Hidden Markov Models (HMMs) are effective for sequential data but traditionally focus on linear structures.
  • Extensions to tree structures exist, yet often fail to capture coupled branches common in biological data.
  • Existing models may struggle with computational efficiency and numerical stability (underflow).

Purpose of the Study:

  • To extend the Hidden Markov Model framework to tree structures with coupled branches.
  • To develop an efficient dynamic programming algorithm for likelihood, decoding, and parameter learning in these models.
  • To provide a robust tool for analyzing complex biological data with inherent lineage dependencies.

Main Methods:

  • Development of a novel dynamic programming algorithm tailored for HMMs on trees with coupled branches.
  • The algorithm addresses likelihood computation, state decoding, and parameter estimation.
  • Polynomial scaling with the number of states and nodes ensures computational feasibility.

    • Main Results:

    • The proposed algorithm efficiently solves HMM problems on trees with coupled branches.
    • The method is computationally feasible and avoids the numerical underflow problem.
    • Demonstrated application on simulated data with proposed self-consistency checks for model validation.

    Conclusions:

    • The developed algorithm provides a significant advancement for HMMs on tree-structured data with coupled branches.
    • This offers a practical and computationally efficient solution for analyzing complex biological systems.
    • The work enhances theoretical understanding and practical application of HMMs in bioinformatics.