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Yang, Aijun; Jiang, Xuejun; Liu, Pengfei; Lin, Jinguan

Sparse Bayesian multinomial probit regression model with correlation prior for high-dimensional data classification. (English) Zbl 1398.62198

Stat. Probab. Lett. 119, 241-247 (2016).
Summary: Selecting a small number of relevant genes for cancer classification has received a great deal of attention in microarray data analysis. In this paper, a sparse Bayesian multinomial probit regression model with correlation prior is proposed. Based on simulated and real datasets, we demonstrate that the proposed method performs better than five other competing methods in terms of variable selection and classification.

MSC:

62J12 Generalized linear models (logistic models)

Keywords:

sparse Bayesian method; multinomial probit model; correlation prior; high-dimensional data classification

Software:

COSA
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Full Text: DOI

References:

[1] Albert, J.; Chib, S., Bayesian analysis of binary and polychotomous response data, J. Amer. Statist. Assoc., 88, 669-679, (1993) · Zbl 0774.62031
[2] Armagan, A.; Dunson, D. B.; Lee, J., Generalized double Pareto shrinkage, Statist. Sinica, 23, 119-143, (2013) · Zbl 1259.62061
[3] Bradley, P., Mangasarian, O., 1998. Feature selection via concave minimization and support vector machines. In: Proceedings of the 15th International Conference on Machine Learning, pp. 82-90.
[4] Chakraborty, S.; Ghosh, M.; Mallick, B. K.; Ghosh, D.; Dougherty, E., Gene expression-based glioma classification using hierarchical Bayesian vector machines, Sankhya, 69, 514-547, (2007) · Zbl 1193.62187
[5] Devroye, L., Non-uniform random variate generation, (1986), Springer-Verlag New York · Zbl 0593.65005
[6] Dudoit, Y.; Yang, H.; Callow, M.; Speed, T., Comparison of discrimination methods for the classification of tumors using gene expression data, J. Amer. Statist. Assoc., 97, 77-87, (2002) · Zbl 1073.62576
[7] Friedman, J. H.; Meulman, J. J., Clustering objects on subsets of attributes (with discussion), J. R. Stat. Soc. Ser. B Stat. Methodol., 66, 1-25, (2004) · Zbl 1060.62064
[8] Hoff, P. D., Model-based subspace clustering, Bayesian Anal., 1, 321-344, (2006) · Zbl 1331.62309
[9] George, E. I.; McCulloch, R. E., Variable selection via Gibbs sampling, J. Amer. Statist. Assoc., 88, 881-889, (1993)
[10] 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, 286, 531-537, (1999)
[11] Guyon, I.; Weston, J.; Barnhill, S.; Vapnik, V., Gene selection for cancer classification using support vector machines, Mach. Learn., 46, 389-422, (2002) · Zbl 0998.68111
[12] Lamnisos, D.; Grin, J. E.; Steel; Mark, F. J., Transdimensional sampling algorithms for Bayesian variable selection in classification problems with many more variables than observations, J. Comput. Graph. Statist., 18, 592-612, (2009)
[13] Mallick, B. K.; Ghosh, D.; Ghosh, M., Bayesian classification of tumors using gene expression data, J. R. Stat. Soc. Ser. B Stat. Methodol., 67, 219-232, (2005) · Zbl 1069.62100
[14] Park, K.; Casella, G., The Bayesian lasso, J. Amer. Statist. Assoc., 103, 681-686, (2009) · Zbl 1330.62292
[15] Sha, N.; Vannucci, M.; Tadesse, M. G.; Brown, P. J.; Dragoni, I.; Davies, N.; Roberts, T. C.; Contestabile, A.; Salmon, N.; Buckley, C.; Falciani, F., Bayesian variable selection in multinomial probit models to identify molecular signatures of disease stage, Biometrics, 60, 812-819, (2004) · Zbl 1274.62428
[16] Strawderman, W. E., Proper Bayes minimax estimators of the multivariate normal mean, Ann. Math. Statist., 42, 385-388, (1971) · Zbl 0222.62006
[17] Yang, A. J.; Li, Y. X.; Tang, N. S.; Lin, J. G., Bayesian variable selection in multinomial probit model for classifying high-dimensional data, Comput. Statist., 30, 2, 399-418, (2015) · Zbl 1317.65049
[18] Yuan, M.; Lin, Y., Efficient empirical Bayes variable selection and estimation in linear models, J. Amer. Statist. Assoc., 472, 1215-1225, (2005) · Zbl 1117.62453
[19] Zhou, X.; Wang, X.; Dougherty, E. R., Multi-class cancer classification using multinomial probit regression with Bayesian gene selection, IEE Proc.-Syst. Biol., 153, 70-78, (2006)
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