# Indian buffet process

## Summary

The Indian Buffet Process (IBP) is a generative model for random "feature allocations" (a "feature allocation" is analogous to a clustering except a given datum can belong to more than one cluster). So while the Chinese Restaurant Process describes a generative model for dividing N integers (customers) into K partitions (table assignments), the IBP describes a generative model for dividing N integers into K subsets, where each integer can occur in an arbitrary number of subsets. These subsets are known as "features" and the entire set is known as a "feature allocation". Note: the IBP has a more formal definition in probability theory where it is known as the marginalized distribution of a Beta process.

## Context

This concept has the prerequisites:

- Chinese restaurant process (The CRP is a useful analogue for understanding the IBP.)
- beta distribution (The IBP is the infinite limit of the beta-Bernoulli distribution.)
- Poisson distribution (The IBP model definition includes the Poisson distribution.)
- gamma function (The PMF for the IBP includes the gamma function.)

## Core resources (read/watch one of the following)

## -Free-

→ The Indian Buffet Process: An Introduction and Review (2011)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Nonparametric Bayesian Models (2009)

## See also

- The IBP linear Gaussian model is an application of the IBP to learning latent binary representations of observe data.