Large-scale Optimization of Partial AUC in a Range of False Positive Rates
Large-scale Optimization of Partial AUC in a Range of False Positive Rates
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DOI：
10.48550/arxiv.2203.01505
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发表时间：
2022-03
期刊：
影响因子：
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通讯作者：
Yao Yao-Yao;Qihang Lin;Tianbao Yang
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文献类型：
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作者：
Yao Yao-Yao;Qihang Lin;Tianbao Yang
ROC曲线下面积(AUC)是机器学习中应用最广泛的分类模型性能指标之一。然而，它总结了ROC空间中所有假阳性率(FPR)的真阳性率(TPR)，其中可能包括在某些应用中没有实际意义的FPR。部分AUC作为AUC的推广，仅总结了特定范围的FPR上的TPR，因此在许多实际情况下是更合适的绩效衡量标准。虽然已经对FPR范围内的局部AUC优化进行了研究，但现有算法不能扩展到大数据，也不适用于深度学习。为了解决这一挑战，我们将问题转化为任意光滑预测函数(例如，深度神经网络)的非光滑凸差(DC)程序，这使得我们能够受到非光滑DC优化的最新进展的启发，开发出基于Moreau包络平滑技术的高效近似梯度下降方法。为了提高大数据处理的效率，我们在算法中使用了一种高效的随机块坐标更新。我们提出的算法也可以用来最小化排序距离损失之和，但这也缺乏有效的求解器。我们建立了寻找近$关键解的复杂性为O(1/\epsilon^6)$。最后，我们通过数值实验验证了所提算法在部分AUC最大化和排序距离损失和最小化两种情况下的有效性。
The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in some applications. The partial AUC, as a generalization of the AUC, summarizes only the TPRs over a specific range of the FPRs and is thus a more suitable performance measure in many real-world situations. Although partial AUC optimization in a range of FPRs had been studied, existing algorithms are not scalable to big data and not applicable to deep learning. To address this challenge, we cast the problem into a non-smooth difference-of-convex (DC) program for any smooth predictive functions (e.g., deep neural networks), which allowed us to develop an efficient approximated gradient descent method based on the Moreau envelope smoothing technique, inspired by recent advances in non-smooth DC optimization. To increase the efficiency of large data processing, we used an efficient stochastic block coordinate update in our algorithm. Our proposed algorithm can also be used to minimize the sum of ranked range loss, which also lacks efficient solvers. We established a complexity of $\tilde O(1/\epsilon^6)$ for finding a nearly $\epsilon$-critical solution. Finally, we numerically demonstrated the effectiveness of our proposed algorithms for both partial AUC maximization and sum of ranked range loss minimization.