Hierarchical Beta Processes and the Indian Buffet Process

Romain Thibaux, Michael I. Jordan
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:564-571, 2007.

Abstract

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

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-thibaux07a, title = {Hierarchical Beta Processes and the Indian Buffet Process}, author = {Thibaux, Romain and Jordan, Michael I.}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {564--571}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/thibaux07a/thibaux07a.pdf}, url = {https://proceedings.mlr.press/v2/thibaux07a.html}, abstract = {We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for the Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known extensions of the Dirichlet process. In particular we define Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algorithms for the Indian buffet process. We also present an application to document classification, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models.} }
Endnote
%0 Conference Paper %T Hierarchical Beta Processes and the Indian Buffet Process %A Romain Thibaux %A Michael I. Jordan %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-thibaux07a %I PMLR %P 564--571 %U https://proceedings.mlr.press/v2/thibaux07a.html %V 2 %X We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for the Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known extensions of the Dirichlet process. In particular we define Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algorithms for the Indian buffet process. We also present an application to document classification, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models.
RIS
TY - CPAPER TI - Hierarchical Beta Processes and the Indian Buffet Process AU - Romain Thibaux AU - Michael I. Jordan BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-thibaux07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 564 EP - 571 L1 - http://proceedings.mlr.press/v2/thibaux07a/thibaux07a.pdf UR - https://proceedings.mlr.press/v2/thibaux07a.html AB - We show that the beta process is the de Finetti mixing distribution underlying the Indian buffet process of [2]. This result shows that the beta process plays the role for the Indian buffet process that the Dirichlet process plays for the Chinese restaurant process, a parallel that guides us in deriving analogs for the beta process of the many known extensions of the Dirichlet process. In particular we define Bayesian hierarchies of beta processes and use the connection to the beta process to develop posterior inference algorithms for the Indian buffet process. We also present an application to document classification, exploring a relationship between the hierarchical beta process and smoothed naive Bayes models. ER -
APA
Thibaux, R. & Jordan, M.I.. (2007). Hierarchical Beta Processes and the Indian Buffet Process. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:564-571 Available from https://proceedings.mlr.press/v2/thibaux07a.html.

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