GEV regression with convex loss applied to imbalanced binary classification

In this paper, we consider the problem of binary classification with imbalanced data. Although this problem has been studied extensively in terms of the classification performance, the probability estimation of both majority and minority class has not yet been well studied. In order to make precise class probability estimation (CPE), we propose a new approach of regression with a recently proposed convex loss function under the framework of generalized linear model. In this model, the generalized extreme value (GEV) distribution is adopted to form the asymmetric link function, which is the key role in binary classification with imbalanced data. Also, we propose a method to estimate the shape parameter in GEV distribution. Experiments on real-world datasets show that our proposed GEV regression has a good classification performance as well as a precise CPE. Besides, comparisons with other optimization algorithms also suggest a high computational efficiency in our algorithm.