The combinatorial structure of beta negative binomial processes
arXiv:1401.0062 · doi:10.3150/15-BEJ729
Abstract
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from conditionally-i.i.d. sequences of Bernoulli processes with a common beta process base measure, in which case the combinatorial structure is described by the Indian buffet process. Our results give a count analogue of the Indian buffet process, which we call a negative binomial Indian buffet process. As an intermediate step toward this goal, we provide a construction for the beta negative binomial process that avoids a representation of the underlying beta process base measure. We describe the key Markov kernels needed to use a NB-IBP representation in a Markov Chain Monte Carlo algorithm targeting a posterior distribution.
Published at http://dx.doi.org/10.3150/15-BEJ729 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
References in corpus (2)
Cited by in corpus (10)
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- Priors for Random Count Matrices Derived from a Family of Negative Binomial Processes
- Posterior distributions for Hierarchical Spike and Slab Indian Buffet processes
- Random Function Priors for Correlation Modeling
- Black-box constructions for exchangeable sequences of random multisets
- On collapsed representation of hierarchical Completely Random Measures