The recent advent of powerful generative models has triggered the renewed development of quantitative measures to assess the proximity of two probability distributions. As the scalar Frechet inception distance remains popular, several methods have explored computing entire curves, which reveal the trade-off between the fidelity and variability of the first distribution with respect to the second one. Several of such variants have been proposed independently and while intuitively similar, their relationship has not yet been made explicit. In an effort to make the emerging picture of generative evaluation more clear, we propose a unification of four curves known respectively as: the precision-recall (PR) curve, the Lorenz curve, the receiver operating characteristic (ROC) curve and a special case of R\'enyi divergence frontiers. In addition, we discuss possible links between PR / Lorenz curves with the derivation of domain adaptation bounds.

翻译：最近出现了强大的基因模型,引发了评估两种概率分布相近程度的量化措施的重新发展。由于卡拉尔·弗雷切特起始距离仍然很受欢迎,一些方法探索了整个曲线的计算,这揭示了第一个分布对第二个分布的忠诚性和可变性之间的权衡。一些这种变体是独立提出的,虽然直觉上是相似的,但它们之间的关系尚未明确。为了使正在形成的基因评估图象更加清晰,我们提议统一四个曲线,分别称为:精确-记号曲线、洛伦茨曲线、接收器操作特性曲线和R\'enyi差异边界的特殊案例。此外,我们讨论了PR/洛伦茨曲线与域调整界限的衍生可能联系。我们讨论了RPR/洛伦茨曲线与域调整界限的衍生关系。