Negative Binomial Process Count and Mixture Modeling

Understand

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process.

• A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling.
• A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples.
• We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions.