Gibbs-type Indian buffet processes

Abstract

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.

27 pages, 5 figures

References in corpus (4)

• Are Gibbs-type priors the most natural generalization of the Dirichlet process?
• Conditional formulae for Gibbs-type exchangeable random partitions
• The combinatorial structure of beta negative binomial processes
• The continuum-of-urns scheme, generalized beta and Indian buffet processes, and hierarchies thereof

Cited by in corpus (3)

• Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis
• Bayesian analysis of product feature allocation models
• Gibbs Partitions, Riemann-Liouville Fractional Operators, Mittag-Leffler Functions, and Fragmentations Derived From Stable Subordinators