Indian Buffet Processes with Power-law Behavior
Yee Whye Teh and Dilan Gorur
In: NIPS 2009, 7-12 Dec 2009, Vancouver, Canada.
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 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 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.