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Bayesian variable selection in multinomial probit model for classifying high-dimensional data

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  • Aijun Yang

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  • Yunxian Li
  • Niansheng Tang
  • Jinguan Lin

Abstract

Selecting a small number of relevant genes for classification has received a great deal of attention in microarray data analysis. While the development of methods for microarray data with only two classes is relevant, developing more efficient algorithms for classification with any number of classes is important. In this paper, we propose a Bayesian stochastic search variable selection approach for multi-class classification, which can identify relevant genes by assessing sets of genes jointly. We consider a multinomial probit model with a generalized $$g$$ g -prior for the regression coefficients. An efficient algorithm using simulation-based MCMC methods are developed for simulating parameters from the posterior distribution. This algorithm is robust to the choice of initial value, and produces posterior probabilities of relevant genes for biological interpretation. We demonstrate the performance of the approach with two well-known gene expression profiling data: leukemia data, lymphoma data, SRBCTs data and NCI60 data. Compared with other classification approaches, our approach selects smaller numbers of relevant genes and obtains competitive classification accuracy based on obtained results. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Aijun Yang & Yunxian Li & Niansheng Tang & Jinguan Lin, 2015. "Bayesian variable selection in multinomial probit model for classifying high-dimensional data," Computational Statistics, Springer, vol. 30(2), pages 399-418, June.
  • Handle: RePEc:spr:compst:v:30:y:2015:i:2:p:399-418
    DOI: 10.1007/s00180-014-0540-z
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    References listed on IDEAS

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    1. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.
    2. Gupta, Mayetri & Ibrahim, Joseph G., 2007. "Variable Selection in Regression Mixture Modeling for the Discovery of Gene Regulatory Networks," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 867-880, September.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, April.
    4. LĂȘ Cao, Kim-Anh & Chabrier, Patrick, 2008. "ofw: An R Package to Select Continuous Variables for Multiclass Classification with a Stochastic Wrapper Method," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i09).
    5. Naijun Sha & Marina Vannucci & Mahlet G. Tadesse & Philip J. Brown & Ilaria Dragoni & Nick Davies & Tracy C. Roberts & Andrea Contestabile & Mike Salmon & Chris Buckley & Francesco Falciani, 2004. "Bayesian Variable Selection in Multinomial Probit Models to Identify Molecular Signatures of Disease Stage," Biometrics, The International Biometric Society, vol. 60(3), pages 812-819, September.
    6. Lee, Yoonkyung & Lin, Yi & Wahba, Grace, 2004. "Multicategory Support Vector Machines: Theory and Application to the Classification of Microarray Data and Satellite Radiance Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 67-81, January.
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    Cited by:

    1. Yang, Aijun & Jiang, Xuejun & Liu, Pengfei & Lin, Jinguan, 2016. "Sparse Bayesian multinomial probit regression model with correlation prior for high-dimensional data classification," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 241-247.

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