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    We developed a novel bottom-up probabilistic model for generating tree structures. This approach better models substructure co-occurrence and handles deep trees compared to top-down methods.

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    Area of Science:

    • Machine Learning
    • Computational Statistics
    • Data Science

    Background:

    • Probabilistic models for tree-structured data are crucial in various fields.
    • Existing top-down generative models have limitations in capturing certain structural properties.

    Purpose of the Study:

    • Introduce a novel compositional, bottom-up probabilistic model for tree generation.
    • Explore the distinct representational capabilities of bottom-up versus top-down approaches.
    • Provide a practical and computationally efficient bottom-up generative model for tree data.

    Main Methods:

    • Developed a recursive probabilistic model with a bottom-up generative process.
    • Defined contextual state transitions from children to parent nodes.
    • Introduced a mixed memory approximation for factorizing the transition matrix.

    Main Results:

    • The bottom-up model effectively models the co-occurrence of substructures in child subtrees.
    • Demonstrated superior performance in handling deep tree structures compared to top-down models.
    • Showcased improved capture of structural information in real-world data with high out-degree trees.

    Conclusions:

    • The proposed bottom-up generative model offers unique advantages over top-down approaches.
    • It provides a practical and computationally feasible method for analyzing tree-structured data.
    • This model serves as a foundational component for developing advanced tree-based machine learning models.