The convergent Indian buffet process

TL;DR

The paper introduces the convergent Indian buffet process (CIBP), a Bayesian nonparametric prior that models a bounded expected number of latent features, addressing limitations of the standard Indian buffet process.

Contribution

It proposes the CIBP, a novel prior with a bounded expected number of features, and provides two alternative representations based on hierarchical distribution and completely random measure.

Findings

CIBP's expected features converge to a finite limit.

CIBP effectively models high-dimensional sparse factors.

Two independent representations of CIBP are developed.

Abstract

We propose a new Bayesian nonparametric prior for latent feature models, which we call the convergent Indian buffet process (CIBP). We show that under the CIBP, the number of latent features is distributed as a Poisson distribution with the mean monotonically increasing but converging to a certain value as the number of objects goes to infinity. That is, the expected number of features is bounded above even when the number of objects goes to infinity, unlike the standard Indian buffet process under which the expected number of features increases with the number of objects. We provide two alternative representations of the CIBP based on a hierarchical distribution and a completely random measure, respectively, which are of independent interest. The proposed CIBP is assessed on a high-dimensional sparse factor model.