Beta-negative binomial process and poisson factor analysis

Mingyuan Zhou; Lauren A. Hannah; David B. Dunson; Lawrence Carin

Beta-negative binomial process and poisson factor analysis

Mingyuan Zhou, Lauren A. Hannah, David B. Dunson, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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 infinite Poisson factor analysis model. A finite approximation for the beta process Lévy 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.

Original language	English (US)
Title of host publication	Journal of Machine Learning Research
Publisher	Microtome [email protected]
Pages	1462-1471
Number of pages	10
State	Published - Jan 1 2012
Externally published	Yes

Cite this

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title = "Beta-negative binomial process and poisson factor analysis",

abstract = "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 infinite Poisson factor analysis model. A finite approximation for the beta process L{\'e}vy 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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N2 - 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 infinite Poisson factor analysis model. A finite approximation for the beta process Lévy 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.

AB - 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 infinite Poisson factor analysis model. A finite approximation for the beta process Lévy 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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BT - Journal of Machine Learning Research

PB - Microtome [email protected]

ER -

Beta-negative binomial process and poisson factor analysis

Abstract

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