Beta-Negative Binomial Process and Poisson Factor Analysis

TL;DR

This paper introduces the beta-negative binomial process as a nonparametric Bayesian prior for infinite Poisson factor analysis, enabling efficient inference and demonstrating promising results in document count matrix factorization.

Contribution

It proposes a novel beta-negative binomial process and its hierarchical structure, extending Bayesian nonparametrics for improved Poisson factor analysis.

Findings

Effective MCMC inference methods developed

Successful application to document count data

Demonstrated advantages over existing models

Abstract

A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" 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 infinite Poisson factor analysis model. A finite approximation for the beta process Levy random measure is constructed for convenient implementation. Efficient MCMC computations are performed with data augmentation and marginalization techniques. Encouraging results are shown on document count matrix factorization.