Indian Buffet Processes with Power-law Behavior

Part of Advances in Neural Information Processing Systems 22 (NIPS 2009)

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Yee Teh, Dilan Gorur


The Indian buffet process (IBP) is an exchangeable distribution over binary matrices 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 \emph{stable-beta process} and deriving the IBP corresponding to it. We find interesting relationships between the stable-beta process and the Pitman-Yor process (another stochastic process used in Bayesian nonparametric models with interesting power-law properties). We show that our power-law IBP is a good model for word occurrences in documents with improved performance over the normal IBP.