Gene Prediction Using Multinomial Probit Regression with Bayesian Gene Selection

A critical issue for the construction of genetic regulatory networks is the identification of network topology from data. In the context of deterministic and probabilistic Boolean networks, as well as their extension to multilevel quantization, this issue is related to the more general problem of expression prediction in which we want to find small subsets of genes to be used as predictors of target genes. Given some maximum number of predictors to be used, a full search of all possible predictor sets is combinatorially prohibitive except for small predictors sets, and even then, may require supercomputing. Hence, suboptimal approaches to finding predictor sets and network topologies are desirable. This paper considers Bayesian variable selection for prediction using a multinomial probit regression model with data augmentation to turn the multinomial problem into a sequence of smoothing problems. There are multiple regression equations and we want to select the same strongest genes for all regression equations to constitute a target predictor set or, in the context of a genetic network, the dependency set for the target. The probit regressor is approximated as a linear combination of the genes and a Gibbs sampler is employed to find the strongest genes. Numerical techniques to speed up the computation are discussed. After finding the strongest genes, we predict the target gene based on the strongest genes, with the coefficient of determination being used to measure predictor accuracy. Using malignant melanoma microarray data, we compare two predictor models, the estimated probit regressors themselves and the optimal fulllogic predictor based on the selected strongest genes, and we compare these to optimal prediction without feature selection.