Learning with Complex Loss Functions and Constraints
Learning with Complex Loss Functions and Constraints
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使用复杂的损失函数和约束进行学习
DOI：
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发表时间：
2018
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通讯作者：
H. Narasimhan
中科院分区：
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作者：
H. Narasimhan
我们发展了一种解决约束分类问题的通用方法，其中损失和约束是根据混淆矩阵的一般函数定义的。我们能够处理复杂的、非线性的损失函数，如F-测量、G-均值或H-均值，以及从预算限制到公平约束，再到复杂评估指标的界限等各种约束。我们的方法建立在Narasimhan等人的框架上。(2015)针对复杂损失的无约束分类，将约束学习问题归结为一系列对代价敏感的学习任务。我们给出了两大类问题的算法，涉及凸性和分数凸性损失，受凸性约束。我们的算法在统计上是一致的，推广了现有的公平分类方法，并且很容易应用于多类问题。在各种任务上的实验证明了我们方法的有效性。
We develop a general approach for solving constrained classification problems, where the loss and constraints are defined in terms of a general function of the confusion matrix. We are able to handle complex, non-linear loss functions such as the F-measure, G-mean or H-mean, and constraints ranging from budget limits, to constraints for fairness, to bounds on complex evaluation metrics. Our approach builds on the framework of Narasimhan et al. (2015) for unconstrained classification with complex losses, and reduces the constrained learning problem to a sequence of cost-sensitive learning tasks. We provide algorithms for two broad families of problems, involving convex and fractional-convex losses, subject to convex constraints. Our algorithms are statistically consistent, generalize an existing approach for fair classification, and readily apply to multiclass problems. Experiments on a variety of tasks demonstrate the efficacy of our methods.