Hierarchical Beta Processes and the Indian Buﬀet Process

by: Romain Thibaux, Michael I Jordan

(2007)

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Abstract

We show that the beta process is the de Finetti mixing distribution underlying the In- dian buﬀet process of [2]. This result shows that the beta process plays the role for the Indian buﬀet process that the Dirichlet pro- cess plays for the Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known ex- tensions of the Dirichlet process. In partic- ular we deﬁne Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algo- rithms for the Indian buﬀet process. We also present an application to document classiﬁ- cation, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models.

@inproceedings{citeulike:2491530, abstract = {We show that the beta process is the de Finetti mixing distribution underlying the In- dian buﬀet process of [2]. This result shows that the beta process plays the role for the Indian buﬀet process that the Dirichlet pro- cess plays for the Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known ex- tensions of the Dirichlet process. In partic- ular we deﬁne Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algo- rithms for the Indian buﬀet process. We also present an application to document classiﬁ- cation, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models.}, author = {Thibaux, Romain and Jordan, Michael I. }, booktitle = {Proceedings of the 11th Conference on Artificial Intelligence and Statistic}, citeulike-article-id = {2491530}, keywords = {bayesian, beta\_process, indian\_buffet\_process, nonparametric, unsupervised\_learning}, posted-at = {2008-03-09 00:34:28}, priority = {0}, title = {Hierarchical Beta Processes and the Indian Buﬀet Process}, year = {2007} }

RIS record

TY - CONF ID - citeulike:2491530 L3 - citeulike-article-id:2491530 TI - Hierarchical Beta Processes and the Indian Buﬀet Process T2 - Proceedings of the 11th Conference on Artificial Intelligence and Statistic N2 - We show that the beta process is the de Finetti mixing distribution underlying the In- dian buﬀet process of [2]. This result shows that the beta process plays the role for the Indian buﬀet process that the Dirichlet pro- cess plays for the Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known ex- tensions of the Dirichlet process. In partic- ular we deﬁne Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algo- rithms for the Indian buﬀet process. We also present an application to document classiﬁ- cation, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models. KW - bayesian KW - beta_process KW - indian_buffet_process KW - nonparametric KW - unsupervised_learning AU - Thibaux, Romain AU - Jordan, Michael PY - 2007/// ER -

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