Sparse Bayesian variable selection in multinomial probit regression model with application to high-dimensional data classification

ABSTRACT

Here we consider a multinomial probit regression model where the number of variables substantially exceeds the sample size and only a subset of the available variables is associated with the response. Thus selecting a small number of relevant variables for classification has received a great deal of attention. Generally when the number of variables is substantial, sparsity-enforcing priors for the regression coefficients are called for on grounds of predictive generalization and computational ease. In this paper, we propose a sparse Bayesian variable selection method in multinomial probit regression model for multi-class classification. The performance of our proposed method is demonstrated with one simulated data and three well-known gene expression profiling data: breast cancer data, leukemia data, and small round blue-cell tumors. The results show that compared with other methods, our method is able to select the relevant variables and can obtain competitive classification accuracy with a small subset of relevant genes.

KEYWORDS:

• High-dimensional data classification
• multinomial probit model
• sparse priors
• stochastic search variable selection.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15

Funding

The authors gratefully acknowledge the financial support of the Natural Science Foundation of China (11501294, 11101432, 11571073), the China Postdoctoral Science Foundation (2015M580374), and the Natural Science Foundation of Jiangsu (BK20141326).