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Indian Buffet Processes with Power-law Behavior

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by Yee Whye Teh , Dilan Görür
Citations:6 - 0 self
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BibTeX

@MISC{Teh_indianbuffet,
    author = {Yee Whye Teh and Dilan Görür},
    title = {Indian Buffet Processes with Power-law Behavior},
    year = {}
}

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Abstract

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. 1

Citations

488 T.S.: A Bayesian analysis of some nonparametric problems - Ferguson - 1973
162 The two-parameter PoissonDirichlet distribution derived from a stable subordinator. Annals of Probability - Pitman, Yor - 1997
160 Gibbs sampling methods for stick–breaking priors - Ishwaran, James - 2001
129 Poisson processes - Kingman - 1993
122 Infinite latent feature models and the Indian buffet process (Technical report - Griffiths, Ghahramani - 2005
83 Selected Studies of the Principle of Relative Frequency in Language - Zipf - 1932
56 Interpolating between types and tokens by estimating power-law generators - Goldwater, Griffiths, et al. - 2006
55 Size-biased sampling of Poisson point processes and excursions - Perman, Pitman, et al. - 1992
52 Nonparametric Bayes Estimators Based on Beta Processes in Models for Life History Data,” The Annals of Statistics - Hjort - 1990
48 A hierarchical Bayesian language model based on Pitman-Yor processes - Teh - 2006
38 Hierarchical Beta Processes and the Indian Buffet Process - Thibaux, Jordan - 2007
35 Modelling dyadic data with binary latent factors - Meeds, Ghahramani, et al. - 2006
34 Stick-breaking construction for the Indian buffet process - Teh, Gorur, et al. - 2007
25 Bayesian Nonparametric Latent Feature Models - Ghahramani, Griffiths, et al. - 2007
25 Completely random measures - Kingman - 1967
24 Shared segmentation of natural scenes using dependent Pitman-Yor processes - Sudderth, Jordan
17 Infinite Sparse Factor Analysis and Infinite Independent Components Analysis - Knowles, Ghahramani - 2007
14 Nonparametric Bayesian estimators for counting processes - Kim - 1999
13 A non-parametric Bayesian method for inferring hidden causes. UAI - Wood, Griffiths, et al. - 2006
11 A choice model with infinitely many latent features - Görür, Jäkel, et al.
8 Simulations of lévy random fields - Wolpert, Ickstadt - 1998
6 Latent features in similarity judgments: A nonparametric Bayesian approach. Neural computation - Navarro, Griffiths - 2008
3 Random discrete distributions derived from subordinators - PERMAN - 1990
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