Receiver Operating Characteristic (ROC) curves are plots of true positive rate versus false positive rate which are used to evaluate binary classification algorithms. Because the Area Under the Curve (AUC) is a constant function of the predicted values, learning algorithms instead optimize convex relaxations which involve a sum over all pairs of labeled positive and negative examples. Naive learning algorithms compute the gradient in quadratic time, which is too slow for learning using large batch sizes. We propose a new functional representation of the square loss and squared hinge loss, which results in algorithms that compute the gradient in either linear or log-linear time, and makes it possible to use gradient descent learning with large batch sizes. In our empirical study of supervised binary classification problems, we show that our new algorithm can achieve higher test AUC values on imbalanced data sets than previous algorithms, and make use of larger batch sizes than were previously feasible.

本文提出了一种新的功能表示方法，用于解决在使用大批量学习场景下原始学习算法太慢的问题，并在监督二分类问题的实验中表明了这种方法对于不平衡的数据集能够获得更高的AUC值，并且可以使用比之前方法更大的批量大小。

使用全对二次铰链损失函数的对数线性梯度下降算法用于非平衡二分类