  Latent feature models are a powerful tool for modeling data with
globally-shared features. Nonparametric exchangeable models such as the Indian
Buffet Process offer modeling flexibility by letting the number of latent
features be unbounded. However, current models impose implicit distributions
over the number of latent features per data point, and these implicit
distributions may not match our knowledge about the data. In this paper, we
demonstrate how the Restricted Indian Buffet Process circumvents this
restriction, allowing arbitrary distributions over the number of features in an
observation. We discuss several alternative constructions of the model and use
the insights gained to develop Markov Chain Monte Carlo and variational methods
for simulation and posterior inference.
