Beta-Negative Binomial Process and Poisson Factor Analysis
Machine Learning
2012-02-07 v4 Methodology
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.
Keywords
Cite
@article{arxiv.1112.3605,
title = {Beta-Negative Binomial Process and Poisson Factor Analysis},
author = {Mingyuan Zhou and Lauren Hannah and David Dunson and Lawrence Carin},
journal= {arXiv preprint arXiv:1112.3605},
year = {2012}
}
Comments
Appearing in AISTATS 2012 (submitted on Oct. 2011)