Receiver Operating Characteristic (ROC) curves are plots of true positive rate versus false positive rate which are useful for evaluating binary classification models, but difficult to use for learning since the Area Under the Curve (AUC) is non-convex. ROC curves can also be used in other problems that have false positive and true positive rates such as changepoint detection. We show that in this more general context, the ROC curve can have loops, points with highly sub-optimal error rates, and AUC greater than one. This observation motivates a new optimization objective: rather than maximizing the AUC, we would like a monotonic ROC curve with AUC=1 that avoids points with large values for Min(FP,FN). We propose a convex relaxation of this objective that results in a new surrogate loss function called the AUM, short for Area Under Min(FP, FN). Whereas previous loss functions are based on summing over all labeled examples or pairs, the AUM requires a sort and a sum over the sequence of points on the ROC curve. We show that AUM directional derivatives can be efficiently computed and used in a gradient descent learning algorithm. In our empirical study of supervised binary classification and changepoint detection problems, we show that our new AUM minimization learning algorithm results in improved AUC and comparable speed relative to previous baselines.

翻译：运行接收器特征( ROC) 曲线是真实正率和假正率的图案, 可用于评估二进制分类模型, 但很难使用这些图案, 因为“ 曲线下区域( AUC) ” (AUC) 是非曲线值。 ROC 曲线也可以用于其他问题, 这些问题有假正率和真实正率, 如变更点检测。 我们显示, 在更普遍的这一大背景下, ROC 曲线可以有循环, 点值为高度次优误率, 而 AUC 则大于一。 这一观察激励了一个新的优化目标: 而不是尽可能扩大 AUC 曲线, 我们希望 AUC=1 的单调 ROC 曲线, 避免给 Min( FP, FN) 带来大值的点数。 我们提议, ROC ROFx 曲线也可以在其它问题上使用一个曲线上的单调调 ROC 。 我们建议, 使这个目标的曲线松松动度松动, 导致一个新的套子损失函数损失函数损失功能,, 短于所有标签或配对,, AUMUCUCS 的顺序需要一种排序的排序。 我们的排序。 我们的比级算法 学习了我们之前的比级的,, 学习一个比级算法 。