Beta-Negative Binomial Process and Poisson Factor Analysis

A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a \multiscoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an innite Poisson factor analysis model. A nite approximation for the beta process L evy random measure is constructed for convenient implementation. Ecient MCMC computations are performed with data augmentation and marginalization techniques. Encouraging results are shown on document count matrix factorization.