Demonstrating the capacity of a Path-Based variational inference formulation for robust hidden Markov modelling of complex and noisy binary trees

Sneha Narayan Naik, Benjamin M. Smith, Andrew F. Laine, Elsa Angelini

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Keywords: hidden Markov model, variational inference, binary tree, generative model

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Abstract: Binary tree structures are prevalent multiple across fields such as procedural modelling, genomics, and image processing. Hidden Markov models (HMMs) provide compact and interpretable representations for these complex and fractal structures. However, current de-facto inference methods involve complex iterations over all sub-trees, implementations that are domain-specific and lack a unified open-source solution. This study explores a novel `paths-of-bifurcations' inference approach to fit hidden Markov parameters on binary trees, compatible with the use of popular modelling packages. Key contributions include: (1) demonstration of procedural modelling for creating a sandbox of synthetic trees for experimentation; (2) comprehensive performance evaluations of our inference procedure on synthetic benchmark trees addressing various challenges: heterogeneity of branch emission distributions, low probability states, small data regimes and noisy observational data; and (3) a practical application to a medical image dataset. The latter showcases the method's ability to reveal insights into branching rules governing the human airway system, with potential implications in disease characterization, airflow analysis, and particle deposition studies. This research provides a step toward robust, scalable and user-friendly generative modelling of binary tree structures with broad interdisciplinary implications.

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Submission Number: 6037