A Fully Bayesian Inference with Gibbs Sampling for Finite and Infinite Discrete Exponential Mixture Models

References

• Alsuroji, R., N. Zamzami, and N. Bouguila. 2018. “Model selection and estimation of a finite shifted-scaled dirichlet mixture model.” In 17th IEEE International Conference on Machine Learning and Applications, ICMLA 2018, Orlando, FL, USA, December 17-20, edited by M. A. Wani, M. M. Kantardzic, M. S. Mouchaweh, J. Gama, and E. Lughofer, 707–2542. IEEE.
   Google Scholar
• Amirkhani, M., N. Manouchehri, and N. Bouguila. 2021. Birth-death MCMC approach for multivariate beta mixture models in medical applications. In Advances and trends in artificial intelligence. artificial intelligence practices, ed. H. Fujita, A. Selamat, J. C.-W. Lin, and M. Ali, 285–96. Cham: Springer International Publishing.
   Google Scholar
• Antoniak, C. E. 1974. Mixtures of dirichlet processes with applications to bayesian nonparametric problems. The Annals of Statistics 2 (6):1152–74. doi:10.1214/aos/1176342871.
   Web of Science ®Google Scholar
• Batista, L., and S. Ratté. 2014. Multi-classifier system for sentiment analysis and opinion mining. In Encyclopedia of social network analysis and mining, ed. R. Alhajj and J. Rokne, 989–98. New York: Springer New York.
   Google Scholar
• Bouguila, N. 2008. Clustering of count data using generalized dirichlet multinomial distributions. IEEE Transactions on Knowledge and Data Engineering 20 (4):462–74. doi:10.1109/TKDE.2007.190726.
   Web of Science ®Google Scholar
• Bouguila, N. 2011. Count data modeling and classification using finite mixtures of distributions. IEEE Transactions on Neural Networks 22 (2):186–98. doi:10.1109/TNN.2010.2091428.
   PubMedGoogle Scholar
• Bouguila, N., and W. Fan. 2020. Mixture models and applications. Springer.
   Google Scholar
• Bouguila, N., and D. Ziou. 2007. Unsupervised learning of a finite discrete mixture: Applications to texture modeling and image databases summarization. Journal of Visual Communication and Image Representation 18 (4):295–309. doi:10.1016/j.jvcir.2007.02.005.
   Web of Science ®Google Scholar
• Bouguila, N., and D. Ziou. 2010. A Dirichlet process mixture of generalized Dirichlet distributions for proportional data modeling. IEEE Transactions on Neural Networks 21 (1):107–22. doi:10.1109/TNN.2009.2034851.
   PubMedGoogle Scholar
• Bouguila, N., D. Ziou, and R. I. Hammoud. 2009. On Bayesian analysis of a finite generalized dirichlet mixture via a Metropolis-within-Gibbs sampling. Pattern Analysis and Applications 12 (2):151–66. doi:10.1007/s10044-008-0111-4.
   Web of Science ®Google Scholar
• Brooks, S. P. 2001. On Bayesian analyses and finite mixtures for proportions. Statistics and Computing 11 (2):179–90. doi:10.1023/A:1008983500916.
   Web of Science ®Google Scholar
• Brown, L. D. 1986. Fundamentals of statistical exponential families with applications in statistical decision theory. Lecture Notes-Monograph Series 9:100–279.
   Google Scholar
• Cai, L. 2010. High-dimensional exploratory item factor analysis by a Metropolis–Hastings Robbins–Monro algorithm. Psychometrika 75 (1):33–57. doi:10.1007/s11336-009-9136-x.
   Web of Science ®Google Scholar
• Church, K. W., and W. A. Gale. 1995. Poisson mixtures. Natural Language Engineering 1 (2):163–90. doi:10.1017/S1351324900000139.
   Google Scholar
• Cornish, R., P. Vanetti, A. Bouchard-Cote, G. Deligiannidis, and A. Doucet. 2019. “Scalable Metropolis–Hastings for exact Bayesian inference with large datasets.” In International Conference on Machine Learning, 1351–60.
   Google Scholar
• DasGupta, A. 2011. The exponential family and statistical applications. In Probability for statistics and machine learning. edited by Anirban DasGupta, 583–612. New York, NY: Springer.
   Google Scholar
• Dhillon, I. S., and D. S. Modha. 2001. Concept decompositions for large sparse text data using clustering. Machine Learning 42 (1/2):143–75. doi:10.1023/A:1007612920971.
   Web of Science ®Google Scholar
• Dias, J. G., and M. Wedel. 2004. An empirical comparison of EM, SEM and MCMC performance for problematic gaussian mixture likelihoods. Statistics and Computing 14 (4):323–32. doi:10.1023/B:STCO.0000039481.32211.5a.
   Web of Science ®Google Scholar
• Elkan, C. 2006. “Clustering documents with an exponential-family approximation of the dirichlet compound multinomial distribution.” In Proceedings of the 23rd International Conference on Machine Learning, ICML ‘06, New York, NY, USA, 289–96. Association for Computing Machinery.
   Google Scholar
• Emanuel, L., and G. T. Herman. 1987. A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography. IEEE Transactions on Medical Imaging 6 (3):185–92. doi:10.1109/TMI.1987.4307826.
   PubMed Web of Science ®Google Scholar
• Escobar, M. D., and M. West. 1995. Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association 90 (430):577–88. doi:10.1080/01621459.1995.10476550.
   Web of Science ®Google Scholar
• Favaro, S., and Y. Whye Teh. 2013. MCMC for normalized random measure mixture models. Statistical Science 28 (3):335–59. doi:10.1214/13-STS422.
   Web of Science ®Google Scholar
• Hartigan, J., and M. Wong. 1979. Algorithm AS 136: A K-Means Clustering Algorithm. Journal of the Royal Statistical Society 28 (1):100–08.
   Google Scholar
• Jain, A. K. 2010. Data clustering: 50 years beyond K-means. Pattern Recognition Letters 31 (8):651–66. doi:10.1016/j.patrec.2009.09.011.
   Web of Science ®Google Scholar
• Jain, S., and R. Neal. 2004. A split-merge markov chain monte carlo procedure for the dirichlet process mixture model. Journal of Computational and Graphical Statistics 13 (1):158–82. doi:10.1198/1061860043001.
   Web of Science ®Google Scholar
• Jegou, H., M. Douze, and C. Schmid. 2009. On the burstiness of visual elements. In 2009 IEEE Conference on Computer Vision and Pattern Recognition, 1169–76.
   Google Scholar
• Katz, S. M. 1996. Distribution of content words and phrases in text and language modelling. Natural Language Engineering 2 (1):15–59. doi:10.1017/S1351324996001246.
   Google Scholar
• Korwar, R. M., and M. Hollander. 1973. Contributions to the theory of dirichlet processes. The Annals of Probability 1 (4):705–11. doi:10.1214/aop/1176996898.
   Web of Science ®Google Scholar
• Lee, P. M. 2012. Bayesian Statistics: An Introduction. Wiley.
   Google Scholar
• MacEachern, S. N., and P. Muller. 1998. Estimating mixture of dirichlet process models. Journal of Computational and Graphical Statistics 7:223–38.
   Web of Science ®Google Scholar
• Madsen, R. E., D. Kauchak, and C. Elkan. 2005. “Modeling WORD BURSTINESS USING THE DIRICHLET DISTRIBUTION.” In Proceedings of the 22nd International Conference on Machine Learning, ICML ‘05, New York, NY, USA, 545?552. Association for Computing Machinery.
   Google Scholar
• Margaritis, D., and S. Thrun. 2001. A bayesian multiresolution independence test for continuous variables. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, 346–53. Morgan Kaufmann Publishers Inc.
   Google Scholar
• Najar, F., N. Zamzami, and N. Bouguila. 2019. “Fake news detection using bayesian inference.” In 2019 IEEE 20th International Conference on Information Reuse and Integration for Data Science (IRI), 389–94.
   Google Scholar
• Najar, F., N. Zamzami, and N. Bouguila. 2020. “Recognition of human interactions in feature films based on infinite mixture of EDCM.” In 2020 International Symposium on Networks, Computers and Communications (ISNCC), 1–6.
   Google Scholar
• Raftery, A. E., and S. M. Lewis. 1992. [Practical markov chain monte carlo]: comment: one long run with diagnostics: implementation strategies for markov chain monte Carlo. Statistical Science 7 (4):493–97. doi:10.1214/ss/1177011143.
   Google Scholar
• Rasmussen, C. E. 1999. The infinite Gaussian mixture model. Advances in Neural Information Processing Systems 12:554–60.
   Google Scholar
• Robert, C. P. 2007. The Bayesian choice. From decision-theoretic foundations to computational implementation. Springer.
   Google Scholar
• Roeder, K., and L. Wasserman. 1997. Practical bayesian density estimation using mixture of normals. Journal of the American Statistical Association 92 (439):894–902. doi:10.1080/01621459.1997.10474044.
   Web of Science ®Google Scholar
• Samuel, K., N. Balakrishnan, and N. L. Johnson. 2000. Continuous multivariate distributions. New York: Wiley-Interscience.
   Google Scholar
• Sorensen, D., and D. Gianola. 2002. Likelihood, Bayesian and MCMC methods in quantitative genetics. Springer.
   Google Scholar
• Train, K. E. 2009. Discrete choice methods with simulation. 2nd ed. Cambridge University Press.
   Google Scholar
• Tsionas, E. G. 2004. Bayesian inference for multivariate gamma distributions. Statistics and Computing 14 (3):223–33. doi:10.1023/B:STCO.0000035302.87186.be.
   Web of Science ®Google Scholar
• Wong, T.-T. 2010. Parameter estimation for generalized Dirichlet distributions from the sample estimates of the first and the second moments of random variables. Computational Statistics & Data Analysis 54 (7):1756–65. doi:10.1016/j.csda.2010.02.008.
   Web of Science ®Google Scholar
• Xuanbo, S., N. Bouguila, and N. Zamzami. 2021. “Covid-19 News Clustering using MCMC-Based Learing of finite EMSD Mixture Models.” In Proceedings of the Thirty-Fourth International Florida Artificial Intelligence Research Society Conference, North Miami Beach, Florida, USA, May 17-19, edited by E. Bell and F. Keshtkar.
   Google Scholar
• Zamzami, N., and N. Bouguila. 2019. A novel scaled Dirichlet-based statistical framework for count data modeling: Unsupervised learning and exponential approximation. Pattern Recognition 95:36–47. doi:10.1016/j.patcog.2019.05.038.
   Web of Science ®Google Scholar
• Zamzami, N., and N. Bouguila. 2020a. High-dimensional count data clustering based on an exponential approximation to the multinomial Beta-Liouville distribution. Information Sciences 524:116–35. doi:10.1016/j.ins.2020.03.028.
   Web of Science ®Google Scholar
• Zamzami, N., and N. Bouguila. 2020b. Probabilistic modeling for frequency vectors using a flexible shifted-scaled dirichlet distribution prior. ACM Trans. Knowl. Discov. Data 14 (6):1–35. doi:10.1145/3406242.
   Web of Science ®Google Scholar
• Zamzami, N., and N. Bouguila. 2022. Sparse count data clustering using an exponential approximation to generalized dirichlet multinomial distributions. IEEE Transactions on Neural Networks and Learning Systems 33 (1):89–102. doi:10.1109/TNNLS.2020.3027539.
   PubMed Web of Science ®Google Scholar