Variational inference for Dirichlet process mixtures

Bayesian Analysis

Volumn 1, Issue 1 A, 2006, Pages 121-144

  Blei, David M ^a   Jordan, Michael I ^b  

^a Carnegie Mellon University ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian computation; Dirichlet processes; Hierarchical models; Image processing; Variational inference

Indexed keywords

EID: 84867186048     PISSN: 19360975     EISSN: 19316690     Source Type: Journal    
DOI: 10.1214/06-BA104     Document Type: Article

References (23)

1. Antoniak, C. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics, 2(6):1152-1174. 122, 124
2. Attias, H. (2000). A variational Bayesian framework for graphical models. In Solla, S., Leen, T., and Muller, K. (eds.), Advances in Neural Information Processing Systems 12, 209-215. Cambridge, MA: MIT Press. 121
3. Barnard, K., Duygulu, P., de Freitas, N., Forsyth, D., Blei, D., and Jordan, M. (2003). Matching words and pictures. Journal of Machine Learning Research, 3:1107-1135. 137
4. Bertsekas, D. (1999). Nonlinear Programming. Nashua, NH: Athena Scientific. 141
5. Blackwell, D. and MacQueen, J. (1973). Ferguson distributions via Pólya urn schemes. The Annals of Statistics, 1(2):353-355. 122, 123
6. Blei, D., Ng, A., and Jordan, M. (2003). Latent Dirichlet allocation. Journal of Machine Learning Research, 3:993-1022. 121
7. Connor, R. and Mosimann, J. (1969). Concepts of independence for proportions with a generalization of the Dirichlet distribution. Journal of the American Statistical Association, 64(325):194-206. 132
8. Escobar, M. and West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90:577-588. 122, 125, 141
9. Ferguson, T. (1973). A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1:209-230. 122, 123, 124
10. Ghahramani, Z. and Beal, M. (2001). Propagation algorithms for variational Bayesian learning. In Leen, T., Dietterich, T., and Tresp, V. (eds.), Advances in Neural Information Processing Systems 13, 507-513. Cambridge, MA: MIT Press. 121, 122, 127, 139, 141
11. Ishwaran, J. and James, L. (2001). Gibbs sampling methods for stick-breaking priors. Journal of the American Statistical Association, 96:161-174. 125, 128, 131
12. Jeon, J., Lavrenko, V., and Manmatha, R. (2003). Automatic image annotation and retrieval using cross-media relevance models. In Proceedings of the 26th Annual International ACM SIGIR conference on Research and Development in Information Retrieval, 119-126. ACM Press. 137
13. Jordan, M., Ghahramani, Z., Jaakkola, T., and Saul, L. (1999). Introduction to vari-ational methods for graphical models. Machine Learning, 37:183-233. 121
14. MacEachern, S. (1994). Estimating normal means with a conjugate style Dirichlet process prior. Communications in Statistics B, 23:727-741. 122, 125, 130
15. MacEachern, S. (1998). Computational methods for mixture of Dirichlet process models. In Dey, D., Muller, P., and Sinha, D. (eds.), Practical Nonparametric and Semiparametric Bayesian Statistics, 23-44. Springer. 125
16. Neal, R. (2000). Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics, 9(2):249-265. 122, 125, 131
17. Opper, M. and Saad, D. (2001). Advanced Mean Field Methods: Theory and Practice. Cambridge, MA: MIT Press. 121
18. Raftery, A. and Lewis, S. (1992). One long run with diagnostics: Implementation strategies for Markov chain Monte Carlo. Statistical Science, 7:493-497. 136
19. Robert, C. and Casella, G. (2004). Monte Carlo Statistical Methods. New York, NY: Springer-Verlag. 133
20. Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statistica Sinica, 4:639-650. 122, 124
21. Wainwright, M. and Jordan, M. (2003). Graphical models, exponential families, and variational inference. Technical Report 649, U.C. Berkeley, Dept. of Statistics. 121, 122, 125, 126, 139, 141
22. Wiegerinck, W. (2000). Variational approximations between mean field theory and the junction tree algorithm. In Boutilier, C. and Goldszmidt, M. (eds.), Proceedings of the 16th Annual Conference on Uncertainty in Artificial Intelligence (UAI-00), 626-633. San Francisco, CA: Morgan Kaufmann Publishers. 121, 141
23. Xing, E., Jordan, M., and Russell, S. (2003). A generalized mean field algorithm for variational inference in exponential families. In Meek, C. and Kjærulff, U. (eds.), Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI-03), 583-591. San Francisco, CA: Morgan Kaufmann Publishers. 141