Gibbs-type Indian buffet processes
This work provides a theoretical extension for feature allocation models in machine learning, enabling flexible modeling of latent structures with varying asymptotic properties, though it is incremental in building on existing processes.
The authors introduced a class of feature allocation models based on Gibbs-type random measures, generalizing the Indian buffet process to include power-law behaviors in latent features, and developed a black-box inference procedure applicable across subclasses.
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.