On Approximations of the Beta Process in Latent Feature Models

TL;DR

This paper proves the asymptotic consistency of finite approximations of the beta process used in latent feature models and introduces an efficient simulation method with empirical validation.

Contribution

It establishes the asymptotic consistency of finite beta process approximations and develops an almost sure simulation method for practical use.

Findings

Finite approximation is asymptotically consistent.

Proposed simulation method is efficient and reliable.

Empirical comparison shows improved performance over existing algorithms.

Abstract

The beta process has recently been widely used as a nonparametric prior for different models in machine learning, including latent feature models. In this paper, we prove the asymptotic consistency of the finite dimensional approximation of the beta process due to Paisley \& Carin (2009). In addition, we derive an almost sure approximation of the beta process. This approximation provides a direct method to efficiently simulate the beta process. A simulated example, illustrating the work of the method and comparing its performance to several existing algorithms, is also included.