Beta-Negative Binomial Process and Poisson Factor Analysis

2011/12/15 by Mingyuan Zhou, Zhou, Mingyuan, Lauren A. Hannah +5 · 7 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1112.3605

openalex publication_date 2011/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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