精确率与召回率之间的最优排序分数是什么？我们总能找到它，而且它很少是 F1
What Is the Optimal Ranking Score Between Precision and Recall? We Can Always Find It and It Is Rarely F1
为视觉任务中普遍使用的 F-beta/F1 指标提供了可替代的排序准则：把「在精确率与召回率之间取折中」形式化为 Kendall 秩相关的优化问题，并给出 beta 的闭式最优解，可直接用于检测、分割等任务的模型排序与基准报告。
原文依据 We frame the problem of finding a tradeoff between two scores as an optimization problem expressed with Kendall rank correlations.
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论依据性能对方法或模型进行排序至关重要，但这一工作并不简单，因为性能本质上是多维的。在分类情形下，精确率与召回率是带有概率解释的分数，二者都重要且互为补充。由这两个分数诱导出的排序常常存在部分矛盾。因此在实际中，在这两种视角之间建立折中以获得单一的整体排序极为有用。过去约五十年间，人们提出采用加权调和平均，即 F-score、F-measure 或 F-beta。一般而言，通过对基础分数取平均，我们得到的分数在数值上处于中间位置。然而，这并不能保证这些分数产生有意义的排序，也不能保证这些排序是各基础分数之间的良好折中。鉴于 F-beta 分数在文献中的普遍使用，有必要加以澄清。具体而言：(1) 我们证明由 F-beta 诱导的排序是有意义的，并定义了精确率诱导排序与召回率诱导排序之间的一条最短路径。(2) 我们将寻找两个分数之间折中的问题表述为一个以 Kendall 秩相关表达的优化问题。我们表明 F1 及其对偏斜不敏感的版本在这方面远非最优。(3) 我们提供理论工具与闭式表达式，可对任意分布或任意一组性能结果求出 beta 的最优值，并在六个案例研究中展示了其用法。代码见 https://github.com/pierard/cvpr-2026-optimal-tradeoff-precision-recall。
英文原文摘要 1645 字符
Ranking methods or models based on their performance is of prime importance but is tricky because performance is fundamentally multidimensional. In the case of classification, precision and recall are scores with probabilistic interpretations that are both important to consider and complementary. The rankings induced by these two scores are often in partial contradiction. In practice, therefore, it is extremely useful to establish a compromise between the two views to obtain a single, global ranking. Over the last fifty years or so, it has been proposed to take a weighted harmonic mean, known as the F-score, F-measure, or F-beta. Generally speaking, by averaging basic scores, we obtain a score that is intermediate in terms of values. However, there is no guarantee that these scores lead to meaningful rankings and no guarantee that the rankings are good tradeoffs between these base scores. Given the ubiquity of F-beta scores in the literature, some clarification is in order. Concretely: (1) We establish that F-beta-induced rankings are meaningful and define a shortest path between precisionand recall-induced rankings. (2) We frame the problem of finding a tradeoff between two scores as an optimization problem expressed with Kendall rank correlations. We show that F1 and its skew-insensitive version are far from being optimal in that regard. (3) We provide theoretical tools and a closed-form expression to find the optimal value for beta for any distribution or set of performances, and we illustrate their use on six case studies. Code is available at https://github.com/pierard/cvpr-2026-optimal-tradeoff-precision-recall.