Restricted Indian buffet processes

Latent feature models are a powerful tool for modeling data with globally-shared features. Nonparametric distributions over exchangeable sets of features, 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 work, 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 apply the insights to develop Markov Chain Monte Carlo and variational methods for simulation and posterior inference.