Hidden markov models with stick-breaking priors

IEEE Transactions on Signal Processing

Volumn 57, Issue 10, 2009, Pages 3905-3917

  Paisley, John ^a   Carin, Lawrence ^a  

^a Duke University   (United States)

Author keywords

Hidden Markov models (HMM); Hierarchical Bayesian modeling; Music analysis; Variational Bayes (VB)

Indexed keywords

BAYESIAN APPROACHES; GIBBS SAMPLING; HIDDEN MARKOV MODELS (HMM); HIERARCHICAL BAYESIAN MODELING; HIERARCHICAL DIRICHLET PROCESS; INFINITE-STATE; MUSIC ANALYSIS; MUSIC RECOMMENDATION; NON-PARAMETRIC; NUMBER OF STATE; OBSERVATION PARAMETER; STATE TRANSITION MATRIX; VARIATIONAL BAYES (VB); VARIATIONAL BAYESIAN; VARIATIONAL SOLUTIONS;

BAYESIAN NETWORKS; COMPUTATIONAL GRAMMARS; COMPUTER MUSIC; OBJECT RECOGNITION;

HIDDEN MARKOV MODELS;

EID: 70349643583     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2024987     Document Type: Article

References (34)

1. D. Aldous, "Exchangeability and related topics," in École d'ete de probabilités de Saint-Flour XIII-1983. Berlin, Germany: Springer, 1985, pp. 1-198.
2. C. E. Antoniak, "Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems," Ann. Statist., vol. 2, pp. 1152-1174, 1974.
3. K. B. Athreya, H. Doss, and J. Sethuraman, "On the convergence of the Markov chain simulation method," Ann. Statist., vol. 24, pp. 69-100, 1996.
4. J. J. Aucouturier and M. Sandler, "Segmentation of musical signals using hidden Markov models," in Proc. 110th Convention Audio Eng. Soc., 2001.
5. L. R. Bahl, F. Jelinek, and R. L. Mercer, "A maximum likelihood approach to continuous speech recognition," IEEE Trans. Pattern Anal. Mach. Intell., vol. 5, no. 2, pp. 179-190, 1983.
6. M. J. Beal, "Variational algorithms for approximate Bayesian inference," Ph.D. thesis, Gatsby Computat. Neurosci. Unit, Univ. College London, London, U.K., 2003.
7. J. A. Bilmes, "A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models," Univ. Calif., Berkeley, Tech. Rep. 97-021, 1998.
8. D. M. Blei and M. I. Jordan, "Variational inference for Dirichlet process mixtures," Bayesian Anal., vol. 1, no. 1, pp. 121-144, 2006.
9. R. J. Boys and D. A. Henderson, "A comparison of reversible jump MCMC algorithms for DNA sequence segmentation using hidden Markov models," Comput. Sci. Statist., vol. 33, pp. 35-49, 2001.
10. P. K. Bharadwaj, P. R. Runkle, and L. Carin, "Target identification with wave-based matched pursuits and hidden Markov models," IEEE Trans. Antennas Propag., vol. 47, pp. 1543-1554, 1999.
11. D. Blackwell and J. B. MacQueen, "Ferguson distributions via Pólya urn schemes," The Ann. Statist., vol. 1, pp. 353-355, 1973.
12. R. J. Connor and J. E. Mosimann, "Concepts of independence for proportions with a generalization of the Dirichlet distribution," J. Amer. Statist. Assoc., vol. 64, pp. 194-206, 1969.
13. S. Davis and P. Mermelstein, "Comparison of parametric representations of monosyllabic word recognition in continuously spoken sentences," IEEE Trans. Acoust. Speech Signal Process., vol. 28, pp. 357-366, 1980.
14. A. Dempster, N. Laird, and D. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Royal Statist. Soc. B, vol. 39, no. 1, pp. 1-38, 1977.
15. R. Durbin, S. R. Eddy, A. Krogh, and G. Mitchison, Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids Cambridge, U.K.: Cambridge Univ. Press, 1999.
16. M. D. Escobar and M. West, "Bayesian density estimation and inference using mixtures," J. Amer. Statist. Assoc., vol. 90, no. 430, pp. 577-588, 1995.
17. T. Ferguson, "A Bayesian analysis of some nonparametric problems," Ann. Statist., vol. 1, pp. 209-230, 1973.
18. P. Halmos, "Random Alms," Ann. Math. Statist., vol. 15, pp. 182-189, 1944.
19. H. Ishwaran and L. F. James, "Gibbs sampling methods for stick-breaking priors," J. Amer. Statist. Assoc., vol. 96, pp. 161-173, 2001.
20. H. Ishwaran and M. Zarepour, "Dirichlet prior sieves in finite normal mixtures," Statistica Sinica, vol. 12, pp. 941-963, 2002.
21. N. Johnson and S. Kotz, Urn Models and Their Applications, ser. Series in Probabil. Math. Statist.. New York: Wiley, 1977.
22. J. S. Liu, "The collapsed Gibbs sampler in Bayesian computations with applications to a gene regulation problem," J. Amer. Statist. Assoc. vol. 89, pp. 958-966, 1994.
23. S. MacEachern and P. Mueller, "Efficient MCMC schemes for robust model extensions using encompassing Dirichelt process mixture models," in Robust Bayesian Anal., F. Ruggeri and D. Rios Insua, Eds. New York: Springer-Verlag, 2000.
24. D. J. C. MacKay, "Ensemble learning for hidden Markov models," Cavendish Lab., Univ. Cambridge, U.K., 1997, Tech. Rep..
25. O. Papaspiliopoulos and G. O. Roberts, "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, vol. 95, no. 1, pp. 169-186, 2008.
26. I. Porteous, A. Ihler, P. Smyth, and M. Welling, "Gibbs sampling for (coupled) infinite mixture models in the stick-breaking representation," in Proc. Conf. Uncertainty in Artif. Intell., Pittsburgh, PA, 2006.
27. K. Ni, Y. Qi, and L. Carin, "Multi-aspect target detection with the infinite hidden Markov model," J. Acoust. Soc. Amer., 2007, To appear.
28. L. R. Rabiner, "A tutorial on hidden Markov models and selected applications in speech recognition," Proc. IEEE, vol. 77, no. 2, 1989.
29. P. R. Runkle, P. K. Bharadwaj, L. Couchman, and L. Carin, "Hidden Markov models for multiaspect target classification," IEEE Trans. Signal Process., vol. 47, pp. 2035-2040, 1999.
30. J. Sethuraman, "A constructive definition of Dirichlet priors," Statistica Sinica, vol. 4, pp. 639-650, 1994.
31. Y. W. Teh, M. I. Jordan, M. J. Beal, and D. M. Blei, "Hierarchical Dirichlet processes," J. Amer. Statist. Assoc., vol. 101, no. 476, pp. 1566-1581, 2006.
32. J. Winn and C. M. Bishop, "Variational message passing," J. Mach. Learn. Res., vol. 6, pp. 661-694, 2005.
33. J. Winn, "Variational message passing and its applications," Ph.D. dissertation, Inference Group, Cavendish Lab., Univ. Cambridge, Cambridge, U.K., 2004.
34. T. T. Wong, "Generalized Dirichlet distribution in Bayesian analysis," Appl. Math. Computat., vol. 97, pp. 165-181, 1998.