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

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g$$\end{document}-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.