Generative models can have distinct mode of failures like mode dropping and low quality samples, which cannot be captured by a single scalar metric. To address this, recent works propose evaluating generative models using precision and recall, where precision measures quality of samples and recall measures the coverage of the target distribution. Although a variety of discrepancy measures between the target and estimated distribution are used to train generative models, it is unclear what precision-recall trade-offs are achieved by various choices of the discrepancy measures. In this paper, we show that achieving a specified precision-recall trade-off corresponds to minimising -divergences from a family we call the {\em PR-divergences }. Conversely, any -divergence can be written as a linear combination of PR-divergences and therefore correspond to minimising a weighted precision-recall trade-off. Further, we propose a novel generative model that is able to train a normalizing flow to minimise any -divergence, and in particular, achieve a given precision-recall trade-off.

翻译：生成模型可能存在不同的失败模式，例如模式丢失和低质量样本，这些无法通过单一标量指标来捕捉。为解决此问题，近期研究提出使用精确率和召回率来评估生成模型，其中精确率衡量样本质量，召回率衡量目标分布的覆盖程度。尽管在训练生成模型时使用了目标分布与估计分布之间的多种差异度量，但不同差异度量选择所实现的精确率-召回率权衡尚不明确。本文表明，实现特定的精确率-召回率权衡等价于最小化一类被称为“精确率-召回率散度”（PR-divergences）的散度族。反之，任何散度均可表示为PR-divergences的线性组合，因此均对应于最小化加权精确率-召回率权衡。此外，我们提出了一种新颖的生成模型，能够训练归一化流以最小化任意散度，特别地，可实现给定的精确率-召回率权衡。