Abstract: Imbalanced data with a high-dimensional input has been widely encountered in many areas of applications. In this situation, it usually becomes essential to reduce redundant variables via model selection to improve the classification performance. However, with a large number of variables, model selection uncertainty is typically very high. To deal with this problem, we present a feasible model averaging procedure based on a cost-sensitive support vector machine (CSSVM) coupled with a cost-sensitive data-driven weight choice criterion for imbalanced classification. Theoretical justifications are provided in two distinct scenarios. When the data exhibits a weak imbalance, we derive a relatively fast uniform convergence rate of the CSSVM solution. In contrast, when the data possesses a strong imbalance, the convergence rate becomes much slower. In both scenarios, an asymptotic optimality of the proposed model averaging approach in the sense of minimizing the out-of-sample hinge loss is established. Moreover, to reduce the computational burden imposed by a large number of candidate models for model averaging, we develop the CSSVM with an L₁-norm penalty to prepare candidate models. Numerical analysis shows the superiority of the proposed model averaging procedure over existing imbalanced classification methods.

Key words and phrases: Asymptotic optimality, imbalanced data, model averaging, uniform convergence rate.