Augment-and-Conquer Negative Binomial Processes
This provides a theoretical unification of models for count data analysis, with incremental improvements in computational efficiency for topic modeling tasks.
The paper developed data augmentation methods for negative binomial distributions to unify count and mixture models under the negative binomial process framework, showing that the gamma-NB process reduces to the hierarchical Dirichlet process with normalization and demonstrating applications in topic modeling.
By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB process can be reduced to the hierarchical Dirichlet process with normalization, highlighting its unique theoretical, structural and computational advantages. A variety of NB processes with distinct sharing mechanisms are constructed and applied to topic modeling, with connections to existing algorithms, showing the importance of inferring both the NB dispersion and probability parameters.