Conference Paper

Indian Buffet Processes with Power-law Behavior.

Conference: Advances in Neural Information Processing Systems 22: 23rd Annual Conference on Neural Information Processing Systems 2009. Proceedings of a meeting held 7-10 December 2009, Vancouver, British Columbia, Canada.
Source: DBLP

ABSTRACT The Indian buffet process (IBP) is an exchangeable distribution over binary ma- trices used in Bayesian nonparametric featural models. In this paper we propose a three-parameter generalization of the IBP exhibiting power-law behavior. We achieve this by generalizing the beta process (the de Finetti measure of the IBP) to the stable-beta process and deriving the IBP corresponding to it. We find interest- ing relationships between the stable-beta process and the Pitman-Yor process (an- other stochastic process used in Bayesian nonparametric models with interesting power-law properties). We derive a stick-breaking construction for the stable-beta process, and find that our power-law IBP is a good model for word occurrences in document corpora.

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    ABSTRACT: The three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let L_n be the number of dishes experimented by the first n customers, and let {\bar K}_n = (1/n)\sum_{i=1}^n K_i where K_i is the number of dishes tried by customer i. The asymptotic distributions of L_n and {\bar K}_n, suitably centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., not generalized) Indian buffet process.


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