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Negative Binomial Process Count and Mixture Modeling.

Mingyuan Zhou, Lawrence Carin

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    Summary
    This summary is machine-generated.

    This study unifies count and mixture modeling using the negative binomial (NB) process, revealing its connections to other distributions and enabling efficient Bayesian inference for advanced applications like topic modeling.

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    Area of Science:

    • Statistical Modeling
    • Machine Learning
    • Computational Statistics

    Background:

    • Count and mixture modeling are distinct statistical problems.
    • Existing models lack a unified framework for both count and mixture data.
    • The negative binomial (NB) process offers a potential unifying structure.

    Purpose of the Study:

    • To unite count and mixture modeling under a single negative binomial (NB) process framework.
    • To explore the theoretical relationships between NB processes and other distributions.
    • To develop efficient Bayesian inference methods for NB processes and their applications.

    Main Methods:

    • Employing a gamma process to model the rate measure of a Poisson process.
    • Utilizing normalization for mixture modeling and marginalization for count modeling.
    • Developing a Poisson-logarithmic bivariate distribution to link NB and Chinese restaurant table distributions.
    • Deriving efficient Bayesian inference techniques.

    Main Results:

    • The negative binomial (NB) process is shown to unify count and mixture modeling.
    • Relationships between NB processes, Dirichlet processes, and other distributions are established.
    • A novel Poisson-logarithmic bivariate distribution is constructed.
    • Efficient Bayesian inference methods are derived, highlighting the NB process's advantages.
    • Various NB processes are constructed and applied to topic modeling.

    Conclusions:

    • The negative binomial (NB) process provides a unified and theoretically advantageous framework for count and mixture modeling.
    • The derived Bayesian inference methods are efficient and applicable to complex problems like topic modeling.
    • Understanding NB dispersion and probability parameters is crucial for model performance.