Negative Binomial Process Count and Mixture Modeling

摘要: The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model rate measure a Poisson process, whose normalization provides random probability for marginalization leads an NB modeling. draw from consists distributed finite number distinct atoms, each which associated with logarithmic data samples. We reveal relationships between various count- mixture-modeling distributions construct Poisson-logarithmic bivariate distribution that connects Chinese restaurant table distributions. Fundamental properties models developed, we derive efficient Bayesian inference. It shown augmentation normalization, gamma-NB can be reduced Dirichlet hierarchical respectively. These highlight theoretical, structural, computational advantages variety processes, including beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB zero-inflated-NB sharing mechanisms, also constructed. applied topic modeling, connections made existing algorithms factor analysis. Example results show importance inferring both dispersion parameters.