are known and have proven useful in Bayesian nonparametrics.

Our focus in the current paper is on an alternative to clustering models that we refer to as *feature allocation models*. While in a clustering model each data point is assigned to one and only one class, in a feature allocation model each data point can belong to multiple groups. It is often natural to view the groups as corresponding to traits or features, such that the notion that a data point belongs to multiple groups corresponds to the point exhibiting multiple traits or features. A Bayesian feature allocation model treats the feature assignments for a given data point as random and subject to posterior inference. A nonparametric Bayesian feature allocation model takes the number of features to also be random and subject to inference.

Research on nonparametric Bayesian feature allocation has been based around a single prior distribution, the Indian buffet process of @griffiths:2006:infinite, which is known to have the beta process as its underlying de Finetti measure [@thibaux:2007:hierarchical]. There does not yet exist a general definition of exchangeability for feature allocation models, nor counterparts of the EPPF or the Kingman paintbox.

In this paper we supply these missing constructions. 