We introduce a novel framework of ranking with abstention, where the learner can abstain from making prediction at some limited cost $c$. We present a extensive theoretical analysis of this framework including a series of $H$-consistency bounds for both the family of linear functions and that of neural networks with one hidden-layer. These theoretical guarantees are the state-of-the-art consistency guarantees in the literature, which are upper bounds on the target loss estimation error of a predictor in a hypothesis set $H$, expressed in terms of the surrogate loss estimation error of that predictor. We further argue that our proposed abstention methods are important when using common equicontinuous hypothesis sets in practice. We report the results of experiments illustrating the effectiveness of ranking with abstention.

翻译：我们提出了一种新颖的带拒绝机制的排序框架，其中学习器可以以有限成本$c$选择放弃预测。我们对该框架进行了广泛的理论分析，针对线性函数族和单隐层神经网络族分别推导了一系列$H-一致性边界。这些理论保证代表了文献中现有的一致性保证最佳结果，即通过预测器的代理损失估计误差来界定其在假设集$H$中的目标损失估计误差的上界。我们进一步论证了在实际应用中使用常见等连续假设集时，所提出的拒绝方法具有重要价值。实验结果表明了带拒绝机制的排序方法的有效性。