We deal with the \textit{selective classification} problem
(supervised-learning problem with a rejection option), where we want to achieve
the best performance at a certain level of coverage of the data. We transform
the original $m$-class classification problem to $(m+1)$-class where the
$(m+1)$-th class represents the model abstaining from making a prediction due
to disconfidence. Inspired by portfolio theory, we propose a loss function for
the selective classification problem based on the doubling rate of gambling.
Minimizing this loss function corresponds naturally to maximizing the return of
a \textit{horse race}, where a player aims to balance between betting on an
outcome (making a prediction) when confident and reserving one's winnings
(abstaining) when not confident. This loss function allows us to train neural
networks and characterize the disconfidence of prediction in an end-to-end
fashion. In comparison with previous methods, our method requires almost no
modification to the model inference algorithm or model architecture.
Experiments show that our method can identify uncertainty in data points, and
achieves strong results on SVHN and CIFAR10 at various coverages of the data.

本文提出了一种基于赌博翻倍率的损失函数，通过将原本的多分类问题转化成带有拒绝选项的问题，实现了在最佳数据覆盖率下的最佳性能。该损失函数不需要对模型推理算法或架构进行修改，可以有效地处理神经网络训练中的不确定性，同时在 SVHN 和 CIFAR10 数据集上实现了较强的结果。