Gibbs-type Indian buffet processes

TL;DR

This paper introduces a generalized class of feature allocation models called Gibbs-type Indian buffet processes, which extend existing models and exhibit power-law behaviors, with practical inference methods and numerical comparisons.

Contribution

It develops a unified framework for Gibbs-type Indian buffet processes, encompassing existing models and enabling flexible power-law feature behaviors with efficient inference methods.

Findings

Gibbs-type IBP generalizes existing models like the Dirichlet and Pitman--Yor IBPs.

Power-law behaviors are observed in the number of latent features.

Numerical experiments demonstrate the utility of different subclasses.

Abstract

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.