# The combinatorial structure of beta negative binomial processes

arXiv: https://arxiv.org/abs/1401.0062 · HTML: https://mlsanity.com/paper/1401.0062/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2013.

## Built on by (most cited first, 1 of 1)

- [A Nonparametric Bayes Approach to Online Activity Prediction](https://mlsanity.com/paper/2401.14722/) (2024)

## Abstract (arXiv)

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.