Bayesian estimation of Dirichlet mixture model with variational inference

Pattern Recognition

Volumn 47, Issue 9, 2014, Pages 3143-3157

  Ma, Zhanyu ^a   Rana, Pravin Kumar ^b   Taghia, Jalil ^b   Flierl, Markus ^b   Leijon, Arne ^b  

^a BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Bayesian estimation; Dirichlet distribution; Extended factorized approximation; Gamma prior; LSF quantization; Mixture modeling; Multiview depth image enhancement; Relative convexity; Variational inference

Indexed keywords

BAYESIAN NETWORKS; IMAGE ENHANCEMENT; MIXTURES; PROBABILITY DISTRIBUTIONS;

BAYESIAN ESTIMATIONS; DIRICHLET DISTRIBUTIONS; EXTENDED FACTORIZED APPROXIMATION; GAMMA PRIOR; LSF QUANTIZATION; MIXTURE MODEL; MULTI-VIEWS; RELATIVE CONVEXITY; VARIATIONAL INFERENCE;

PARAMETER ESTIMATION;

EID: 84900821630     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2014.04.002     Document Type: Article

References (58)

1. K. Fukunaga Introduction to Statistical Pattern Recognition 1990 Academic Press, San Diego, CA, USA
2. A.K. Jain, R.P.W. Duin, and J. Mao Statistical pattern recognition a review IEEE Trans. Pattern Anal. Mach. Intell. 22 2000 4 37
3. C.M. Bishop Pattern Recognition and Machine Learning 1st ed. 2006 Springer New York
4. J.M. Bernardo, and A. Smith Bayesian Theory, Wiley Series in Probability and Statistics 2000 John Wiley & Sons Ltd. Chichester
5. J.D. Banfield, and A.E. Raftery Model-based Gaussian and non-Gaussian clustering Biometrics 49 3 1993 803 821
6. Y. Ji, C. Wu, P. Liu, J. Wang, and K.R. Coombes Application of beta-mixture models in bioinformatics Bioinform. Appl. Note 21 2005 2118 2122
7. Z. Ma, Non-Gaussian statistical models and their applications (Ph.D. thesis), KTH - Royal Institute of Technology, 2011
8. Z. Ma, and A. Leijon Bayesian estimation of beta mixture models with variational inference IEEE Trans. Pattern Anal. Mach. Intell. 33 11 2011 2160 2173
9. Z. Ma, A.E. Teschendorff, A variational Bayes beta mixture model for feature selection in DNA methylation studies, J. Bioinform. Comput. Biol. 11 (4) (2013) 1350005 (19 pp.)
10. N. Bouguila, D. Ziou, and J. Vaillancourt Unsupervised learning of a finite mixture model based on the Dirichlet distribution and its application IEEE Trans. Image Process. 13 11 2004 1533 1543
11. D. Blei, Probabilistic models of text and images (Ph.D. thesis), Univ. of California, Berkeley, 2004
12. W. Fan, N. Bouguila, and D. Ziou Variational learning for finite Dirichlet mixture models and applications IEEE Trans. Neural Netw. Learn. Syst. 23 5 2012 762 774
13. Z. Ma, A. Leijon, and W.B. Kleijn Vector quantization of LSF parameters with a mixture of Dirichlet distributions IEEE Trans. Audio Speech Lang. Process. 21 2013 1777 1790
14. G.J. McLachlan, and D. Peel Finite Mixture Models 2000 Wiley, New York, USA
15. D.M. Blei, and M.I. Jordan Variational inference for Dirichlet process mixtures Bayesian Anal. 1 2005 121 144
16. P. Orbanz, Y.W. Teh, Bayesian nonparametric models, Encyclopedia of Machine Learning, 2010, pp 81-89
17. Z. Ghahramani, Bayesian non-parametrics and the probabilistic approach to modelling. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 371 (1984) (2013) 20110553
18. M.I. Jordan, Z. Ghahramani, T.S. Jaakkola, and L.K. Saul An introduction to variational methods for graphical models Mach. Learn. 37 2 1999 183 233
19. T.S. Jaakkola, Tutorial on variational approximation methods, in: Advanced Mean Field Methods: Theory and Practice, MIT Press, Cambridge, MA, USA, 2000, pp. 129-159
20. T.S. Jaakkola, Tutorial on variational approximation methods, in: Advances in Mean Field Methods, MIT Press, Cambridge, MA, USA, 2001, pp. 129-159
21. D.M. Blei, J.D. Lafferty, Correlated topic models, in: Advances in Neural Information Processing Systems, MIT Press, Cambridge, MA, USA, 2006, pp. 147 - 154
22. D.M. Blei, and J.D. Lafferty A correlated topic model of Science Ann. Appl. Stat. 1 2007 17 35
23. M. Braun, and J. McAuliffe Variational inference for large-scale models of discrete choice J. Am. Stat. Assoc. 105 2010 324 335
24. M. Hoffman, D. Blei, P. Cook, Bayesian nonparametric matrix factorization for recorded music, in: Proceedings of International Conference on Machine Learning, 2010
25. Z. Ma, A. Leijon, Modeling speech line spectral frequencies with Dirichlet mixture models, in: Proceedings of INTERSPEECH, 2010, pp. 2370-2373
26. M. Tanimoto, M.P. Tehrani, T. Fujii, and T. Yendo Free-viewpoint TV IEEE Signal Process. Mag. 28 1 2011 67 76
27. R. Ksantini, D. Ziou, B. Colin, and F. Dubeau Weighted pseudometric discriminatory power improvement using a Bayesian logistic regression model based on a variational method IEEE Trans. Pattern Anal. Mach. Intell. 30 2 2008 253 266
28. P.J. Bickel, and K.A. Doksum Mathematical Statistics: Basic Ideas and Selected Topics 2007 Pearson Prentice Hall, New Jersey, USA
29. J.A. Palmer, Relative convexity, Technical Report, UCSD, 2003
30. Z. Ma, A. Leijon, Beta mixture models and the application to image classification, in: Proceedings of IEEE International Conference on Image Processing (ICIP), 2009, pp. 2045 -2048
31. R.J. Connor, and J.E. Mosimann Concepts of independence for proportions with a generalization of the Dirichlet distribution J. Am. Stat. Assoc. 64 325 1969 194 206
32. P.K. Rana, Z. Ma, J. Taghia, M. Flierl, Multiview depth map enhancement by variational Bayes inference estimation of Dirichlet mixture models, in: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2013, pp. 1528-1532
33. K.K. Paliwal, W.B. Kleijn, Quantization of LPC parameters, in: Speech Coding and Synthesis, Elsevier, Amsterdam, The Netherlands, pp. 433-466, 1995
34. J. Lindblom, and J. Samuelsson Bounded support Gaussian mixture modeling of speech spectra IEEE Trans. Speech Audio Process. 11 1 2003 88 99
35. A.D. Subramaniam, and B.D. Rao PDF optimized parametric vector quantization of speech line spectral frequencies IEEE Trans. Speech Audio Process. 11 2 2003 130 142
36. S. Chatterjee, T.V. Sreenivas, Low complexity wideband LSF quantization using GMM of uncorrelated Gaussian mixtures, in: 16th European Signal Processing Conference (EUSIPCO 2008), 2008
37. J.S. Garofolo, L.F. Lamel, W.M. Fisher, J.G. Fiscus, D.S. Pallett, DARPA TIMIT acoustic-phonetic continuous speech corpus CD-ROM, NIST speech disc 1-1.1, NASA STI/Recon Technical Report N 93, 1993, p. 27403
38. S. So, and K.K. Paliwal Empirical lower bound on the bitrate for the transparent memoryless coding of wideband LPC parameters IEEE Signal Process. Lett. 13 9 2006 569 572
39. A.A. Neath, and J.E. Cavanaugh The Bayesian information criterion background, derivation, and applications Wiley Interdiscip. Rev. Comput. Stat. 4 2 2012 199 203
40. MPEG, Call for proposals on 3D video coding technology, Technical Report N12036, ISO/IEC JTC1/SC29/WG11, Geneva, Switzerland, March 2011
41. H. Urey, K. Chellappan, E. Erden, and P.A. Surman State of the art in stereoscopic and autostereoscopic displays Proc. IEEE 99 4 2011 540 555
42. K. Müller, P. Merkle, and T. Wiegand 3-D video representation using depth maps Proc. IEEE 99 4 2011 643 656
43. M. Flierl, and B. Girod Multiview video compression IEEE Signal Process. Mag. 24 6 2007 66 76
44. A. Smolic, K. Müller, N. Stefanoski, J. Ostermann, A. Gotchev, G. Akar, G. Triantafyllidis, and A. Koz Coding algorithms for 3DTV-A survey IEEE Trans. Circuits Syst. Video Technol. 17 11 2007 1606 1621
45. C. Fehn, Depth-image-based rendering (DIBR), compression, and transmission for a new approach on 3D-TV, vol. 5291, SPIE, 2004, pp. 93-104
46. D. Scharstein, and R. Szeliski A taxonomy and evaluation of dense two-frame stereo correspondence algorithms Int. J. Comput. Vision 47 2002 7 42
47. Y. Boykov, and V. Kolmogorov An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision IEEE Trans. Pattern Anal. Mach. Intell. 26 9 2004 1124 1137
48. P. Felzenszwalb, D. Huttenlocher, Efficient belief propagation for early vision, in: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, Washington, DC, USA, 2004, pp. 261-268
49. P.K. Rana, M. Flierl, Depth consistency testing for improved view interpolation, in: Proceedings of the IEEE International Workshop on Multimedia Signal Processing, St. Malo, France, 2010, pp. 384-389
50. P.K. Rana, J. Taghia, M. Flierl, A variational Bayesian inference framework for multiview depth image enhancement, in: Proceedings of the IEEE International Symposium on Multimedia, Irvine, California, USA, 2012, pp. 183-190
51. G. Wyszecki, and W. Stiles Color Science: Concepts and Methods, Quantitative Data and Formulae 2nd ed. 2000 John Wiley & Sons New York, NY, USA
52. M. Tanimoto, T. Fujii, K. Suzuki, N. Fukushima, Y. Mori, Reference Softwares for Depth Estimation and View Synthesis, Technical Report M15377, ISO/IEC JTC1/SC29/WG11, Archamps, France, April 2008
53. R.I. Hartley, and A. Zisserman Multiple View Geometry in Computer Vision 2nd ed. 2004 Cambridge University Press Cambridge, UK
54. G. Wolberg Digital Image Warping 1st ed. 1994 IEEE Computer Society Press Los Alamitos, CA, USA
55. L. McMillan, An image-based approach on three-dimensional computer graphics (Ph.D. thesis), University of North Carolina, Chapel Hill, 1997
56. W.R. Mark, Post-rendering 3D image warping: visibility, reconstruction, and performance for depth-image (Ph.D. thesis), University of North Carolina, 1999
57. M. Bertalmio, A. Bertozzi, G. Sapiro, Navier-Stokes, fluid dynamics, and image and video inpainting, in: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, Kauai, HI, USA, 2001, pp. 355-362
58. MPEG, View Synthesis Software Manual, ISO/IEC JTC1/SC29/WG11, release 3.5, September 2009.