  We investigate a class of feature allocation models that generalize the
Indian buffet process and are parameterized by Gibbs-type random measures. Two
existing classes are contained as special cases: the original two-parameter
Indian buffet process, corresponding to the Dirichlet process, and the stable
(or three-parameter) Indian buffet process, corresponding to the Pitman--Yor
process. Asymptotic behavior of the Gibbs-type partitions, such as power laws
holding for the number of latent clusters, translates into analogous
characteristics for this class of Gibbs-type feature allocation models. Despite
containing several different distinct subclasses, the properties of Gibbs-type
partitions allow us to develop a black-box procedure for posterior inference
within any subclass of models. Through numerical experiments, we compare and
contrast a few of these subclasses and highlight the utility of varying
power-law behaviors in the latent features.
