Stochastic Optimization of Areas Under Precision-Recall Curves with Provable Convergence
Stochastic Optimization of Areas Under Precision-Recall Curves with Provable Convergence
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发表时间：
2021-04
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通讯作者：
Qi Qi-Qi;Youzhi Luo;Zhao Xu;Shuiwang Ji;Tianbao Yang
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作者：
Qi Qi-Qi;Youzhi Luo;Zhao Xu;Shuiwang Ji;Tianbao Yang
ROC曲线下面积（AUROC）和精确度-召回率曲线（AUPRC）是评估不平衡问题分类性能的常用指标。与AUROC相比，AUPRC是一个更适合高度不平衡数据集的度量。虽然AUROC的随机优化已被广泛研究，但AUPRC的原则性随机优化却很少被探索。在这项工作中，我们提出了一种原则性的技术方法来优化深度学习的AUPRC。我们的方法是基于最大化的平均精度（AP），这是一个无偏点估计AUPRC。我们把目标转换成一个{\it dependent composition functions}的总和，内部函数依赖于外部水平的随机变量。我们提出了有效的自适应和非自适应随机算法命名为SOAP {\它可证明收敛保证温和的条件下}，利用最近的进展，随机组合优化。在图像和图形数据集上的大量实验结果表明，我们提出的方法在AUPRC方面的不平衡问题上优于现有方法。据我们所知，我们的工作是第一次尝试优化AUPRC与可证明的收敛。SOAP已在libAUC库中实现，地址为~\url{https：//libauc.org/}。
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 stochastic optimization of AUROC has been studied extensively, principled stochastic 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 cast the objective into a sum of {\it dependent compositional functions} with inner functions dependent on random variables of the outer level. We propose efficient adaptive and non-adaptive stochastic algorithms named SOAP with {\it provable convergence guarantee under mild conditions} by leveraging recent advances in stochastic compositional optimization. Extensive experimental results on image and graph datasets demonstrate that our proposed method outperforms prior methods on imbalanced problems in terms of AUPRC. To the best of our knowledge, our work represents the first attempt to optimize AUPRC with provable convergence. The SOAP has been implemented in the libAUC library at~\url{https://libauc.org/}.