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

Author

Listed:
  • Luai Al Labadi

    (University of Toronto)

  • Mahmoud Zarepour

    (University of Ottawa)

Abstract

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.

Suggested Citation

  • Luai Al Labadi & Mahmoud Zarepour, 2018. "On Approximations of the Beta Process in Latent Feature Models: Point Processes Approach," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 59-79, February.
    • Handle: RePEc:spr:sankha:v:80:y:2018:i:1:d:10.1007_s13171-017-0103-9
    DOI: 10.1007/s13171-017-0103-9
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    References listed on IDEAS

    as
    1. Lee, Jaeyong & Kim, Yongdai, 2004. "A new algorithm to generate beta processes," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 441-453, October.
    2. Yongdai Kim & Lancelot James & Rafael Weissbach, 2012. "Bayesian analysis of multistate event history data: beta-Dirichlet process prior," Biometrika, Biometrika Trust, vol. 99(1), pages 127-140.
    3. Luai Al Labadi & Mahmoud Zarepour, 2014. "Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 341-357, June.
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