Beta-Negative Binomial Process and Poisson Factor Analysis

Mingyuan Zhou, Lauren Hannah, David Dunson, Lawrence Carin
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:1462-1471, 2012.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-zhou12c, title = {Beta-Negative Binomial Process and Poisson Factor Analysis}, author = {Zhou, Mingyuan and Hannah, Lauren and Dunson, David and Carin, Lawrence}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {1462--1471}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/zhou12c/zhou12c.pdf}, url = {https://proceedings.mlr.press/v22/zhou12c.html}, 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.} }
Endnote
%0 Conference Paper %T Beta-Negative Binomial Process and Poisson Factor Analysis %A Mingyuan Zhou %A Lauren Hannah %A David Dunson %A Lawrence Carin %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-zhou12c %I PMLR %P 1462--1471 %U https://proceedings.mlr.press/v22/zhou12c.html %V 22 %X 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.
RIS
TY - CPAPER TI - Beta-Negative Binomial Process and Poisson Factor Analysis AU - Mingyuan Zhou AU - Lauren Hannah AU - David Dunson AU - Lawrence Carin BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-zhou12c PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 1462 EP - 1471 L1 - http://proceedings.mlr.press/v22/zhou12c/zhou12c.pdf UR - https://proceedings.mlr.press/v22/zhou12c.html AB - 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. ER -
APA
Zhou, M., Hannah, L., Dunson, D. & Carin, L.. (2012). Beta-Negative Binomial Process and Poisson Factor Analysis. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:1462-1471 Available from https://proceedings.mlr.press/v22/zhou12c.html.

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