Sparse Bayesian hierarchical modeling of high-dimensional clustering problems

Journal of Multivariate Analysis

Volumn 101, Issue 7, 2010, Pages 1728-1737

  Lian, Heng ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Dirichlet process; Markov chain Monte Carlo; Sequential sampling; Sparsity prior

Indexed keywords

EID: 77952009834     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2010.03.009     Document Type: Article

References (32)

1. Golub T.R., Slonim D.K., Tamayo P., Huard C., Gaasenbeek M., Mesirov J.P., Coller H., Loh M.L., Downing J.R., Caligiuri M.A., Bloomfield C.D., Lander E.S. Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 1999, 286(5439):531-537.
2. Banfield J.D., Raftery A.E. Model-based Gaussian and non-Gaussian clustering. Biometrics 1993, 49(3):803-821.
3. Fraley C., Raftery A.E. Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 2002, 97(458):611-631.
4. Luan Y., Li H. Clustering of time-course gene expression data using a mixed-effects model with B-splines. Bioinformatics 2003, 19:474-482.
5. Pan W., Shen X. Penalized model-based clustering with application to variable selection. Journal of Machine Learning Research 2007, 8:1145-1164.
6. Ma P., Zhong W. Penalized clustering of large scale functional data with multiple covariates. Journal of the American Statistical Association 2008, 103(482):625-636.
7. Tibshirani R. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society Series B-Methodological 1996, 58(1):267-288.
8. George E.I., McCulloch R.E. Variable selection via Gibbs sampling. Journal of the American Statistical Association 1993, 88(423):881-889.
9. George E.I., McCulloch R.E. Approaches for Bayesian variable selection. Statistica Sinica 1997, 7(2):339-373.
10. Friedman J.H., Meulman J.J. Clustering objects on subsets of attributes. Journal of the Royal Statistical Society Series B-Statistical Methodology 2004, 66:815-839.
11. Liu J., Zhang J., Palumbo M., Lawrence C. Bayesian clustering with variable and transformation selection. Bayesian Statistics 2003, 7:249-275.
12. Tadesse M.G., Sha N., Vannucci M. Bayesian variable selection in clustering high-dimensional data. Journal of the American Statistical Association 2005, 100(470):602-617.
13. Kim S., Tadesse M.G., Vannucci M. Variable selection in clustering via Dirichlet process mixture models. Biometrika 2006, 93(4):877-893.
14. Hoff P. Model-based subspace clustering. Bayesian Analysis 2006, 1:321-344.
15. Lucas J., Carvalho C., Wang Q., Bild A., Nevins J.R., West M. Sparse statistical modelling in gene expression genomics. Bayesian Inference for Gene Expression and Proteomics 2006, 155-176. Cambridge University Press.
16. Seo D.M., Goldschmidt-Clermont P.J., West M. Of mice and men: sparse statistical modeling in cardiovascular genomics. Annals of Applied Statistics 2007, 1(1):152-178.
17. Carvalho C., Chang J., Lucas J., Nevins J., Wang Q., West M. High-dimensional sparse factor modeling: applications in gene expression genomics. Journal of the American Statistical Association 2008, 103(484):1438-1456.
18. Antoniak C.E. Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. The Annals of Statistics 1974, 2(6):1152-1174.
19. Ibrahim J., Chen M.H., Gray R.J. Bayesian models for gene expression with DNA microarray data. Journal of the American Statistical Association 2002, 97(457):88-99.
20. H.A. Chipman, E.I. George, R.E. McCulloch, BART: Bayesian additive regression trees. Annals of Applied Statistics, 2010 (in press).
21. Rodriguez A., Dunson D.B., Gelfand A.E. The nested Dirichlet process. Journal of the American Statistical Association 2008, 103(483):1131-1144.
22. Nott D.J. Predictive performance of Dirichlet process shrinkage methods in linear regression. Computational Statistics & Data Analysis 2008, 52(7):3658-3669.
23. Dudoit S., Fridlyand J., Speed T.P. Comparison of discrimination methods for the classification of tumors using gene expression data. Journal of the American Statistical Association 2002, 97(457):77-87.
24. Thomas J.G., Olson J.M., Tapscott S.J., Zhao L.P. An efficient and robust statistical modeling approach to discover differentially expressed genes using genomic expression profiles. Genome Research 2001, 11(7):1227-1236.
25. C. Fraley, A.E. Raftery, MCLUST version 3 for R: normal mixture modeling and model-based clustering. Technical Report no. 504, Department of Statistics, University of Washington (2006).
26. Bickel P.J., Levina E. Some theory for Fisher's linear discriminant function, naive Bayes', and some alternatives when there are many more variables than observations. Bernoulli 2004, 10(6):989-1010.
27. Tibshirani R., Hastie T., Narasimhan B., Chu G. Class prediction by nearest shrunken centroids, with applications to DNA microarrays. Statistical Science 2003, 18(1):104-117.
28. Neal R.M. Markov chain sampling methods for Dirichlet process mixture. Journal of Computational and Graphical Statistics 2000, 9(2):249-265.
29. Jain S., Neal R.M. A split-merge Markov chain Monte Carlo procedure for the dirichlet process mixture model. Journal of Computational and Graphical Statistics 2004, 13(1):158-182.
30. van Dyk D.A., Park T. Partially collapsed Gibbs samplers: theory and methods. Journal of the American Statistical Association 2008, 103(482):790-796.
31. Escobar M.D., West M. Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association 1995, 90(430):577-588.
32. Stephens M. Dealing with label switching in mixture models. Journal of the Royal Statistical Society Series B-Statistical Methodology 2000, 62:795-809.