Areas under ROC (AUROC) and precision-recall curves (AUPRC) are common metrics for evaluating classification performance for imbalanced problems. Compared with AUROC, AUPRC is a more appropriate metric for highly imbalanced datasets. While direct optimization of AUROC has been studied extensively, optimization of AUPRC has been rarely explored. In this work, we propose a principled technical method to optimize AUPRC for deep learning. Our approach is based on maximizing the averaged precision (AP), which is an unbiased point estimator of AUPRC. We show that the surrogate loss function for AP is highly non-convex and more complicated than that of AUROC. We cast the objective into a sum of dependent compositional functions with inner functions dependent on random variables of the outer level. We propose efficient adaptive and non-adaptive stochastic algorithms with provable convergence guarantee under mild conditions by using recent advances in stochastic compositional optimization. Extensive experimental results on graphs and image datasets demonstrate that our proposed method outperforms prior methods on imbalanced problems. To the best of our knowledge, our work represents the first attempt to optimize AUPRC with provable convergence.

本文提出一种基于AUPRC pipeline的技术方法，采用SOAP采样算法来提高分类性能，并利用最新的随机组合优化技术进行优化。该方法在图像和图形数据集上的实验结果表明，在AUPRC方面，我们的方法优于先前的方法。这是首次尝试通过证明收敛性来优化AUPRC。

带有可证收敛性的精确度-召回曲线下面积的随机优化