Title: On Approximations of the Beta Process in Latent Feature Models: Point Processes Approach

Author(s): Luai Al Labadi and Mahmoud Zarepour
Issue: Volume 80 Series A Part 1 Year 2018
Pages: 59 -- 79
In recent times, the beta process has 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 and Carin (2009). In particular, we show that this finite approximation converges in distribution to the Ferguson and Klass representation of the beta process. We implement this approximation to derive asymptotic properties of functionals of the finite dimensional beta process. In addition, we derive an almost sure approximation of the beta process. This new 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.
AMS (2000) subject classification. Primary 62F15, 62G20; Secondary 60G51.
Keywords and phrases: Beta process, Ferguson and Klass representation, Finite dimensional approximation, Latent feature models, Simulation