Bayesian feature selection for classification with possibly large number of classes

In what follows, we introduce two Bayesian models for feature selection in high-dimensional data, specifically designed for the purpose of classification. We use two approaches to the problem: one which discards the components which have “almost constant” values (Model 1) and another which retains the components for which variations in-between the groups are larger than those within the groups (Model 2). We assume that p⪢np⪢n, i.e. the number of components p is much larger than the number of samples n, and that only few of those p components are useful for subsequent classification. We show that particular cases of the above two models recover familiar variance or ANOVA-based component selection. When one has only two classes and features are a priori independent, Model 2 reduces to the Feature Annealed Independence Rule (FAIR) introduced by Fan and Fan (2008) and can be viewed as a natural generalization of FAIR to the case of L>2L>2 classes. The performance of the methodology is studies via simulations and using a biological dataset of animal communication signals comprising 43 groups of electric signals recorded from tropical South American electric knife fishes.