skip to main content
10.5555/3104482.3104594guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
Article

Variational inference for stick-breaking beta process priors

Published: 28 June 2011 Publication History

Abstract

We present a variational Bayesian inference algorithm for the stick-breaking construction of the beta process. We derive an alternate representation of the beta process that is amenable to variational inference, and present a bound relating the truncated beta process to its infinite counterpart. We assess performance on two matrix factorization problems, using a non-negative factorization model and a linear-Gaussian model.

References

[1]
Conrad, DF, Jakobsson, M, Coop, G, Wen, X, Wall, JD, Rosenberg, NA, and Pritchard, JK. A worldwide survey of haplotype variation and linkage disequilibrium in the human genome. Nature Genetics, 38:1251-1260, 2006.
[2]
Doshi-Velez, F., Miller, K.T., Van Gael, J., and Teh, Y.W. Variational inference for the Indian buffet process. In AISTATS, 2009.
[3]
Ghahramani, Z., Griffiths, T.L., and Sollich, P. Bayesian nonparametric latent feature models. Bayesian Statistics, 2007.
[4]
Griffiths, T.L. and Ghahramani, Z. Infinite latent feature models and the Indian buffet process. In NIPS, 2006.
[5]
Hjort, N.L. Nonparametric bayes estimators based on beta processes in models for life history data. Annals of Statistics, 18(3):1259-1294, 1990.
[6]
Ishwaran, H. and James, L.F. Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96(453):161-173, 2001.
[7]
Jordan, M.I., Ghahramani, Z., Jaakkola, T., and Saul, L.K. An introduction to variational methods for graphical models. Machine Learning, 37:183-233, 1999.
[8]
Lee, D.D. and Seung, H.S. Algorithms for non-negative matrix factorization. In NIPS, 2001.
[9]
Paisley, J., Zaas, A., Ginsburg, G., Woods, C., and Carin, L. A stick-breaking construction of the beta process. In ICML, 2010.
[10]
Sethuraman, J. A constructive definition of Dirichlet priors. Statistica Sinica, 4:639-650, 1994.
[11]
Teh, Y., Gorur, D., and Ghahramani, Z. Stick-breaking construction for the Indian buffet process. In AISTATS, 2007.
[12]
Thibaux, R. and Jordan, M.I. Hierarchical beta processes and the Indian buffet process. In AISTATS, 2007.
[13]
Williamson, C., Wang, C., Heller, K., and Blei, D. The IBP compound Dirichlet process and its application to focused topic modeling. In ICML, 2010.
[14]
Zhou, M., Chen, H., Paisley, J., Ren, L., Sapiro, G., and Carin, L. Non-parametric Bayesian dictionary learning for sparse image representations. In NIPS, 2009.

Cited By

View all
  1. Variational inference for stick-breaking beta process priors

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image Guide Proceedings
      ICML'11: Proceedings of the 28th International Conference on International Conference on Machine Learning
      June 2011
      1216 pages
      ISBN:9781450306195

      Sponsors

      • NSF: National Science Foundation
      • Xerox
      • Microsoft Research: Microsoft Research
      • Yahoo!
      • Amazon: Amazon.com

      Publisher

      Omnipress

      Madison, WI, United States

      Publication History

      Published: 28 June 2011

      Qualifiers

      • Article

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)0
      • Downloads (Last 6 weeks)0
      Reflects downloads up to 16 Oct 2024

      Other Metrics

      Citations

      Cited By

      View all

      View Options

      View options

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media