In ranking applications, AUC^ROC is widely used in measuring the performance of a discriminative model. But this is possible only if the labels are binary, like in $\{0,1\}$, as AUC^ROC is undefined for non-binary labels. In modelling applications where the labels are not from $\{0,1\}$ but are probabilities of membership $(p,1-p)$ to the binary classes, we generally use other metrics.

In this paper, we propose a metric A^Ratio which can be used on binary as well as probabilistic labels. We prove that it is exactly equal to AUC^ROC for binary labels. We also prove that it extends the same semantics as AUC^ROC for probabilistic labels. We extend the confusion matrix for probabilistic labels and redefine metrics like precision, recall and F₁-score. We define Acc^Ratioand show that it is equivalent to area under the precision–recall curve for non-binary probabilistic labels.

在排名应用中，AUC ^ROC被广泛用于衡量判别模型的性能。但这只有在标签是二进制的情况下才有可能，例如$\{0,1\}$，因为 AUC ^ROC对于非二进制标签是未定义的。在标签不是来自的建模应用程序中$\{0,1\}$ 但是是成员的概率 $(磷,1-磷)$ 对于二进制类，我们通常使用其他指标。

在本文中，我们提出了一个度量 A ^Ratio，它可以用于二进制和概率标签。我们证明它完全等于二进制标签的AUC ^ROC。我们还证明，它扩展了与 AUC ^ROC相同的概率标签语义。我们扩展了概率标签的混淆矩阵，并重新定义了精度、召回率和 F ₁分数等指标。我们定义了 Acc ^Ratio并表明它相当于非二元概率标签的精度-召回曲线下的面积。