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September 2020 Gibbs-type Indian Buffet Processes
Creighton Heaukulani, Daniel M. Roy
Bayesian Anal. 15(3): 683-710 (September 2020). DOI: 10.1214/19-BA1166


We investigate a class of feature allocation models that generalize the Indian buffet process and are parameterized by Gibbs-type random measures. Two existing classes are contained as special cases: the original two-parameter Indian buffet process, corresponding to the Dirichlet process, and the stable (or three-parameter) Indian buffet process, corresponding to the Pitman–Yor process. Asymptotic behavior of the Gibbs-type partitions, such as power laws holding for the number of latent clusters, translates into analogous characteristics for this class of Gibbs-type feature allocation models. Despite containing several different distinct subclasses, the properties of Gibbs-type partitions allow us to develop a black-box procedure for posterior inference within any subclass of models. Through numerical experiments, we compare and contrast a few of these subclasses and highlight the utility of varying power-law behaviors in the latent features.


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Creighton Heaukulani. Daniel M. Roy. "Gibbs-type Indian Buffet Processes." Bayesian Anal. 15 (3) 683 - 710, September 2020.


Published: September 2020
First available in Project Euclid: 19 June 2019

MathSciNet: MR4132646
Digital Object Identifier: 10.1214/19-BA1166


Vol.15 • No. 3 • September 2020
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