Nonparametric additive model with grouped lasso and maximizing area under the ROC curve

An ROC (Receiver Operating Characteristic) curve is a popular tool in the classification of two populations. The nonparametric additive model is used to construct a classifier which is estimated by maximizing the U-statistic type of empirical AUC (Area Under Curve). In particular, the sparsity situation is considered in the sense that only a small number of variables is significant in the classification, so it is demanded that lots of noisy variables will be removed. Some theoretical result on the necessity of variable selection under the sparsity condition is provided since the AUC of the classifier from maximization of empirical AUC is not guaranteed to be optimal. To select significant variables in the classification, the grouped lasso which has been widely used when groups of parameters need to be either selected or discarded simultaneously is used. In addition, the performance of the proposed method is evaluated by numerical studies including simulation and real data examples compared with other existing approaches.